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How to Draw Particle Diagrams

Written By Sunday, March 6, 2022 Add Comment Edit

Learning Objectives

By the finish of the section, you will be able to:

  • Explain the rules for drawing a complimentary-body diagram
  • Construct complimentary-body diagrams for different situations

The first pace in describing and analyzing most phenomena in physics involves the conscientious drawing of a free-body diagram. Complimentary-trunk diagrams have been used in examples throughout this chapter. Remember that a free-body diagram must only include the external forces acting on the torso of interest. Once we accept drawn an accurate free-body diagram, we can apply Newton's first police if the body is in equilibrium (counterbalanced forces; that is, [latex] {F}_{\text{net}}=0 [/latex]) or Newton's second law if the body is accelerating (unbalanced force; that is, [latex] {F}_{\text{cyberspace}}\ne 0 [/latex]).

In Forces, we gave a brief problem-solving strategy to help y'all understand free-body diagrams. Here, we add some details to the strategy that will help you in constructing these diagrams.

Problem-Solving Strategy: Constructing Free-Trunk Diagrams

Observe the following rules when amalgam a gratis-torso diagram:

  1. Depict the object under consideration; it does not have to be artistic. At first, you may want to draw a circle around the object of interest to be sure you focus on labeling the forces acting on the object. If you are treating the object equally a particle (no size or shape and no rotation), represent the object every bit a point. We oftentimes place this bespeak at the origin of an xy-coordinate system.
  2. Include all forces that deed on the object, representing these forces as vectors. Consider the types of forces described in Common Forces—normal force, friction, tension, and spring strength—likewise as weight and applied force. Do not include the net force on the object. With the exception of gravity, all of the forces we accept discussed require straight contact with the object. However, forces that the object exerts on its environment must non exist included. We never include both forces of an activeness-reaction pair.
  3. Convert the complimentary-torso diagram into a more detailed diagram showing the x– and y-components of a given strength (this is oftentimes helpful when solving a problem using Newton'south first or second law). In this case, place a squiggly line through the original vector to show that it is no longer in play—information technology has been replaced past its 10– and y-components.
  4. If at that place are two or more than objects, or bodies, in the trouble, depict a separate complimentary-body diagram for each object.

Note: If at that place is acceleration, we do not direct include it in the gratuitous-trunk diagram; nonetheless, it may assist to bespeak acceleration outside the gratis-body diagram. Y'all can characterization it in a unlike colour to signal that it is separate from the free-body diagram.

Let's use the problem-solving strategy in drawing a free-body diagram for a sled. In (Figure)(a), a sled is pulled by forcefulness P at an angle of [latex] 30\text{°} [/latex]. In part (b), we show a free-body diagram for this situation, as described by steps 1 and ii of the problem-solving strategy. In part (c), we show all forces in terms of their x– and y-components, in keeping with step three.

Figure a shows a sled of 15 kg. An arrow labeled P pointing right and up forms an angle of 30 degrees with the horizontal. Figure b is a free body diagram with P, N pointing up and w pointing down. Figure c is a free body diagram with P, N, w and two components of P: Px pointing right and Py pointing up.

Figure v.31 (a) A moving sled is shown as (b) a complimentary-body diagram and (c) a free-body diagram with force components.

Example

Two Blocks on an Inclined Plane

Construct the complimentary-body diagram for object A and object B in (Effigy).

Strategy

We follow the four steps listed in the problem-solving strategy.

Solution

We start by creating a diagram for the first object of interest. In (Figure)(a), object A is isolated (circled) and represented by a dot.

Figure a shows two objects on an inclined plane, sloping down to the left. Object A is on top of object B. A free body diagram shows T pointing right and up, parallel to the plane, N subscript BA pointing left and up, perpendicular to the plane, f subscript BA pointing left and down, parallel to the plane and w subscript A pointing vertically down. W subscript A is weight of block A, T is tension, N subscript BA is normal force exerted by B on A, f subscript BA is friction force exerted by B on A. Figure b shows the objects on the slope in the same manner. A free body diagram has f subscript B and f subscript AB pointing right and up, parallel to the slope, N subscript B pointing left and up perpendicular to the slope, w subscript B pointing vertically down and N subscript AB pointing down and right, perpendicular to the slope. W subscript B is weight of block B, N subscript AB is normal force exerted by A on B, N subscript B is normal force exerted by the incline plane on B. f subscript AB is friction force exerted by A on B. f subscript B is friction force exerted by the incline plane on B.

Figure 5.32 (a) The free-torso diagram for isolated object A. (b) The gratuitous-trunk diagram for isolated object B. Comparison the ii drawings, we see that friction acts in the reverse direction in the two figures. Because object A experiences a strength that tends to pull information technology to the right, friction must act to the left. Because object B experiences a component of its weight that pulls it to the left, downwardly the incline, the friction force must oppose it and deed up the ramp. Friction e'er acts opposite the intended direction of motion.

We now include any forcefulness that acts on the body. Here, no applied strength is nowadays. The weight of the object acts as a strength pointing vertically downwards, and the presence of the cord indicates a strength of tension pointing away from the object. Object A has one interface and hence experiences a normal force, directed away from the interface. The source of this force is object B, and this normal force is labeled appropriately. Since object B has a tendency to slide downward, object A has a trend to slide upwards with respect to the interface, so the friction [latex] {f}_{\text{BA}} [/latex] is directed downward parallel to the inclined airplane.

As noted in step 4 of the problem-solving strategy, we and then construct the gratuitous-body diagram in (Figure)(b) using the same approach. Object B experiences two normal forces and two friction forces due to the presence of 2 contact surfaces. The interface with the inclined plane exerts external forces of [latex] {N}_{\text{B}} [/latex] and [latex] {f}_{\text{B}} [/latex], and the interface with object B exerts the normal force [latex] {North}_{\text{AB}} [/latex] and friction [latex] {f}_{\text{AB}} [/latex]; [latex] {Due north}_{\text{AB}} [/latex] is directed abroad from object B, and [latex] {f}_{\text{AB}} [/latex] is opposing the tendency of the relative motion of object B with respect to object A.

Significance

The object under consideration in each function of this trouble was circled in grayness. When yous are first learning how to describe free-body diagrams, y'all will find it helpful to circle the object before deciding what forces are acting on that item object. This focuses your attention, preventing yous from considering forces that are non acting on the body.

Case

Two Blocks in Contact

A force is applied to two blocks in contact, as shown.

Strategy

Draw a free-trunk diagram for each block. Be sure to consider Newton's 3rd police at the interface where the two blocks touch.

Two squares are shown in contact with each other. The left one is smaller and is labeled m1. The right one is bigger and is labeled m2. An arrow pointing right towards m1 is labeled F.

Solution

Figure shows two free body diagrams. The first one shows arrow A subscript 21 pointing left and arrow F pointing right. The second one shows arrow A 12 pointing right. Both diagrams also have arrows pointing up and down.

Significance[latex] {\overset{\to }{A}}_{21} [/latex] is the activeness force of cake 2 on block one. [latex] {\overset{\to }{A}}_{12} [/latex] is the reaction force of cake 1 on cake 2. We employ these free-trunk diagrams in Applications of Newton'southward Laws.

Example

Block on the Table (Coupled Blocks)

A block rests on the table, as shown. A light rope is attached to information technology and runs over a pulley. The other terminate of the rope is attached to a second cake. The two blocks are said to be coupled. Block [latex] {m}_{2} [/latex] exerts a forcefulness due to its weight, which causes the system (2 blocks and a string) to accelerate.

Strategy

We assume that the string has no mass so that nosotros do not have to consider information technology as a separate object. Describe a gratuitous-body diagram for each block.

Figure shows block m1 placed on a table. A string attached to it runs over a pulley and down the right side of the table. A block m2 is suspended from it. An arrow a1 points right and an arrow a2 points down.

Solution

Figure a shows block m1. An arrow labeled m1g point upwards from it, an arrow N points downwards and an arrow T points right. Figure b shows block m2. An arrow T points upwards from it and an arrow m2g points downwards.

Significance

Each cake accelerates (observe the labels shown for [latex] {\overset{\to }{a}}_{1} [/latex] and [latex] {\overset{\to }{a}}_{2} [/latex]); however, bold the string remains taut, they advance at the same rate. Thus, we have [latex] {\overset{\to }{a}}_{ane}={\overset{\to }{a}}_{two} [/latex]. If we were to go along solving the problem, we could but call the acceleration [latex] \overset{\to }{a} [/latex]. Also, we use two free-body diagrams because we are ordinarily finding tension T, which may require usa to use a system of 2 equations in this type of problem. The tension is the same on both [latex] {grand}_{1}\,\text{and}\,{chiliad}_{ii} [/latex].

Check Your Understanding

(a) Draw the free-body diagram for the state of affairs shown. (b) Redraw information technology showing components; use x-axes parallel to the two ramps.

Two carts are tied with a rope which goes over a pulley on top of a hill. Each cart rests on one slope of the hill on either side of the pulley. The cart on the left is labeled m1 and the one on the right is labeled m2.

Effigy a shows a complimentary torso diagram of an object on a line that slopes down to the right. Arrow T from the object points right and up, parallel to the slope. Pointer N1 points left and up, perpendicular to the slope. Pointer w1 points vertically downwards. Pointer w1x points left and downwards, parallel to the gradient. Pointer w1y points correct and down, perpendicular to the gradient. Figure b shows a gratuitous body diagram of an object on a line that slopes down to the left. Arrow N2 from the object points correct and upwardly, perpendicular to the slope. Arrow T points left and upwardly, parallel to the slope. Arrow w2 points vertically down. Arrow w2y points left and down, perpendicular to the slope. Arrow w2x points correct and down, parallel to the gradient.

View this simulation to predict, qualitatively, how an external force volition affect the speed and direction of an object'south motility. Explain the effects with the assist of a free-body diagram. Employ free-body diagrams to depict position, velocity, acceleration, and forcefulness graphs, and vice versa. Explain how the graphs relate to one some other. Given a scenario or a graph, sketch all four graphs.

Summary

  • To draw a free-body diagram, we draw the object of involvement, describe all forces acting on that object, and resolve all force vectors into ten– and y-components. We must draw a separate free-body diagram for each object in the problem.
  • A free-body diagram is a useful means of describing and analyzing all the forces that deed on a trunk to determine equilibrium according to Newton's first law or acceleration according to Newton's second police.

Key Equations

Net external strength [latex] {\overset{\to }{F}}_{\text{cyberspace}}=\sum \overset{\to }{F}={\overset{\to }{F}}_{1}+{\overset{\to }{F}}_{2}+\text{⋯} [/latex]
Newton's first law [latex] \overset{\to }{v}=\,\text{abiding when}\,{\overset{\to }{F}}_{\text{net}}=\overset{\to }{0}\,\text{Due north} [/latex]
Newton'due south second law, vector form [latex] {\overset{\to }{F}}_{\text{net}}=\sum \overset{\to }{F}=m\overset{\to }{a} [/latex]
Newton'southward 2nd police, scalar grade [latex] {F}_{\text{net}}=ma [/latex]
Newton's 2d law, component form [latex] \sum {\overset{\to }{F}}_{ten}=m{\overset{\to }{a}}_{x}\text{,}\,\sum {\overset{\to }{F}}_{y}=chiliad{\overset{\to }{a}}_{y},\,\text{and}\,\sum {\overset{\to }{F}}_{z}=1000{\overset{\to }{a}}_{z}. [/latex]
Newton'south second law, momentum form [latex] {\overset{\to }{F}}_{\text{net}}=\frac{d\overset{\to }{p}}{dt} [/latex]
Definition of weight, vector form [latex] \overset{\to }{w}=m\overset{\to }{k} [/latex]
Definition of weight, scalar form [latex] w=mg [/latex]
Newton's 3rd police [latex] {\overset{\to }{F}}_{\text{AB}}=\text{−}{\overset{\to }{F}}_{\text{BA}} [/latex]
Normal forcefulness on an object resting on a

horizontal surface, vector form

 [latex] \overset{\to }{Due north}=\text{−}m\overset{\to }{g} [/latex]
Normal force on an object resting on a

horizontal surface, scalar form

 [latex] N=mg [/latex]
Normal force on an object resting on an

inclined plane, scalar form

 [latex] Due north=mg\text{cos}\,\theta [/latex]
Tension in a cable supporting an object

of mass m at rest, scalar form

 [latex] T=w=mg [/latex]

Conceptual Questions

In completing the solution for a problem involving forces, what do we do after amalgam the gratuitous-body diagram? That is, what do nosotros employ?

If a book is located on a table, how many forces should be shown in a costless-body diagram of the book? Describe them.

Two forces of different types: weight interim downward and normal force interim up

If the book in the previous question is in free fall, how many forces should exist shown in a complimentary-body diagram of the book? Describe them.

Problems

A brawl of mass m hangs at residual, suspended by a string. (a) Sketch all forces. (b) Describe the free-body diagram for the ball.

A car moves along a horizontal road. Describe a free-body diagram; exist certain to include the friction of the road that opposes the forward motion of the motorcar.

A free body diagram shows a vector F subscript e pointing right, vector N pointing up, vector f pointing left and arrow w pointing down.

A runner pushes against the track, equally shown. (a) Provide a complimentary-trunk diagram showing all the forces on the runner. (Hint: Place all forces at the middle of his body, and include his weight.) (b) Requite a revised diagram showing the xy-component grade.

A picture of a man running towards the right is shown. An arrow labeled F points up and right from the floor towards his foot.

The traffic light hangs from the cables every bit shown. Describe a free-trunk diagram on a coordinate plane for this situation.

Figure shows a traffic light hanging from a horizontal cable by three other cables, T1, T2 and T3. T1 hangs down and right making an angle of 41 degrees with the horizontal cable. T2 hangs down and left, making an angle of 63 degrees with the horizontal cable. These meet at a point and T3 hangs vertically down from here. The light is attached to T3. A vector pointing down from the light is labeled w equal to 200 newtons.

Figure shows coordinate axes. Three arrows radiate out from the origin. T1, labeled 41 degrees points up and left. T2, labeled 63 degrees points up and right. T3 equal to w equal to 200 N is along the negative y axis.

Additional Problems

Two small forces, [latex] {\overset{\to }{F}}_{i}=-2.forty\hat{i}-half dozen.10t\hat{j} [/latex] North and [latex] {\overset{\to }{F}}_{2}=8.50\hat{i}-nine.70\hat{j} [/latex] N, are exerted on a rogue asteroid by a pair of space tractors. (a) Find the cyberspace force. (b) What are the magnitude and direction of the net force? (c) If the mass of the asteroid is 125 kg, what acceleration does it feel (in vector course)? (d) What are the magnitude and direction of the dispatch?

Two forces of 25 and 45 N act on an object. Their directions differ by [latex] lxx\text{°} [/latex]. The resulting dispatch has magnitude of [latex] ten.0\,{\text{m/s}}^{ii}. [/latex] What is the mass of the trunk?

A force of 1600 N acts parallel to a ramp to push a 300-kg piano into a moving van. The ramp is inclined at [latex] 20\text{°} [/latex]. (a) What is the acceleration of the pianoforte up the ramp? (b) What is the velocity of the piano when it reaches the top if the ramp is four.0 m long and the piano starts from balance?

Draw a gratuitous-body diagram of a diver who has entered the water, moved downward, and is acted on by an upward force due to the water which balances the weight (that is, the diver is suspended).

A free body diagram with arrow F pointing up and arrow w pointing down.

For a swimmer who has simply jumped off a diving lath, assume air resistance is negligible. The swimmer has a mass of 80.0 kg and jumps off a board 10.0 m in a higher place the water. 3 seconds after entering the water, her downward motility is stopped. What average upward force did the water exert on her?

(a) Find an equation to determine the magnitude of the net force required to stop a machine of mass m, given that the initial speed of the car is [latex] {v}_{0} [/latex] and the stopping distance is x. (b) Find the magnitude of the cyberspace force if the mass of the car is 1050 kg, the initial speed is 40.0 km/h, and the stopping distance is 25.0 1000.

a. [latex] {F}_{\text{net}}=\frac{m({v}^{two}-{five}_{0}{}^{two})}{2x} [/latex]; b. 2590 N

A sailboat has a mass of [latex] ane.50\,×\,{10}^{iii} [/latex] kg and is acted on by a force of [latex] 2.00\,×\,{ten}^{3} [/latex] Due north toward the east, while the wind acts behind the sails with a force of [latex] 3.00\,×\,{x}^{iii} [/latex] Due north in a direction [latex] 45\text{°} [/latex] due north of e. Find the magnitude and management of the resulting acceleration.

Find the dispatch of the body of mass 10.0 kg shown below.

Three arrow radiate outwards from a circle labeled m. F1, equal to 10 N, points vertically down. F2, equal to 20 N, points up and right, making an angle of minus 37 degrees with the positive y axis. F3, equal to 10 N, points up and left, making an angle of 37 degrees with the positive y axis.

[latex] \begin{array}{cc} {\overset{\to }{F}}_{\text{cyberspace}}=4.05\chapeau{i}+12.0\chapeau{j}\text{N}\hfill \\ {\overset{\to }{F}}_{\text{cyberspace}}=m\overset{\to }{a}⇒\overset{\to }{a}=0.405\hat{i}+i.xx\hat{j}\,{\text{yard/s}}^{2}\hfill \end{array} [/latex]

A trunk of mass 2.0 kg is moving along the 10-axis with a speed of iii.0 thou/s at the instant represented below. (a) What is the acceleration of the body? (b) What is the trunk's velocity x.0 s later? (c) What is its displacement after ten.0 s?

Three arrow radiate outwards from a circle labeled m. F1, equal to 50 N, points up and right, making an angle of 37 degrees with the x axis. F2, equal to 30 N, points left and down, making an angle of minus 30 degrees with the negative y axis. F3, equal to 80 N, points left.

Forcefulness [latex] {\overset{\to }{F}}_{\text{B}} [/latex] has twice the magnitude of strength [latex] {\overset{\to }{F}}_{\text{A}}. [/latex] Find the direction in which the particle accelerates in this figure.

Two arrows radiate outwards from a circle labeled m. F subscript A points right. F subscript B points down and left, making an angle of 45 degrees with the horizontal.

Shown below is a body of mass i.0 kg under the influence of the forces [latex] {\overset{\to }{F}}_{A} [/latex], [latex] {\overset{\to }{F}}_{B} [/latex], and [latex] m\overset{\to }{g} [/latex]. If the body accelerates to the left at [latex] twenty\,{\text{m/due south}}^{ii} [/latex], what are [latex] {\overset{\to }{F}}_{A} [/latex] and [latex] {\overset{\to }{F}}_{B} [/latex]?

Three arrows radiate outwards from a point labeled m. F subscript A points left and down, making an angle of 60 degrees with the negative x axis. F subscript B points left and up, making an angle of minus 30 degrees with the negative x axis. Vector mg points vertically down.

A force acts on a motorcar of mass m so that the speed v of the car increases with position 10 equally [latex] v=k{x}^{two} [/latex], where g is constant and all quantities are in SI units. Find the forcefulness acting on the car as a function of position.

[latex] F=2kmx [/latex]; First, have the derivative of the velocity function to obtain [latex] a=2kx [/latex]. And then apply Newton'southward second police force [latex] F=ma=m(2kx)=2kmx [/latex].

A 7.0-N forcefulness parallel to an incline is practical to a 1.0-kg crate. The ramp is tilted at [latex] xx\text{°} [/latex] and is frictionless. (a) What is the dispatch of the crate? (b) If all other conditions are the same only the ramp has a friction forcefulness of one.nine N, what is the dispatch?

Two boxes, A and B, are at rest. Box A is on level ground, while box B rests on an inclined plane tilted at bending [latex] \theta [/latex] with the horizontal. (a) Write expressions for the normal force acting on each block. (b) Compare the 2 forces; that is, tell which 1 is larger or whether they are equal in magnitude. (c) If the angle of incline is [latex] 10\text{°} [/latex], which force is greater?

a. For box A, [latex] {N}_{\text{A}}=mg [/latex] and [latex] {North}_{\text{B}}=mg\,\text{cos}\,\theta [/latex]; b. [latex] {N}_{\text{A}}>{N}_{\text{B}} [/latex] considering for [latex] \theta <xc\text{°} [/latex], [latex] \text{cos}\,\theta <1 [/latex]; c. [latex] {N}_{\text{A}}>{N}_{\text{B}} [/latex] when [latex] \theta =10\text{°} [/latex]

A mass of 250.0 g is suspended from a spring hanging vertically. The leap stretches half dozen.00 cm. How much will the bound stretch if the suspended mass is 530.0 m?

Every bit shown beneath, ii identical springs, each with the spring abiding xx Northward/yard, support a fifteen.0-N weight. (a) What is the tension in jump A? (b) What is the amount of stretch of spring A from the residuum position?

Figure shows two identical springs hanging side by side. Their lower ends are brought together and support a weight. Each spring makes an angle of 30 degrees with the vertical.

a. 8.66 Northward; b. 0.433 m

Shown below is a 30.0-kg block resting on a frictionless ramp inclined at [latex] threescore\text{°} [/latex] to the horizontal. The block is held by a leap that is stretched 5.0 cm. What is the strength constant of the bound?

Figure shows a surface sloping down and left, making an angle of 60 degrees with the horizontal. An object of 30 kg hangs from a spring and rests on the slope.

In building a house, carpenters use nails from a big box. The box is suspended from a jump twice during the day to measure out the usage of nails. At the beginning of the day, the spring stretches 50 cm. At the finish of the 24-hour interval, the bound stretches thirty cm. What fraction or percentage of the nails have been used?

0.xl or xl%

A force is applied to a cake to move it upward a [latex] 30\text{°} [/latex] incline. The incline is frictionless. If [latex] F=65.0\,\text{N} [/latex] and [latex] M=five.00\,\text{kg} [/latex], what is the magnitude of the acceleration of the block?

Figure shows a surface sloping down and right, making an angle of 30 degrees with the horizontal. A box labeled M rests on it. An arrow labeled F points horizontally left towards the box. The angle formed by the arrow and the slope is 30 degrees.

Two forces are applied to a 5.0-kg object, and information technology accelerates at a rate of [latex] 2.0\,{\text{chiliad/s}}^{2} [/latex] in the positive y-direction. If ane of the forces acts in the positive x-direction with magnitude 12.0 N, discover the magnitude of the other forcefulness.

The block on the right shown beneath has more mass than the block on the left ([latex] {m}_{two}>{m}_{1} [/latex]). Describe costless-body diagrams for each block.

A pulley is attached to the ceiling. A rope goes over it. A block of mass m1 is attached to the left end of the rope and another block labeled m2 is attached to the right end of the rope. M2 hangs lower than m1.

Challenge Bug

If two tugboats pull on a disabled vessel, equally shown here in an overhead view, the disabled vessel will exist pulled along the direction indicated by the result of the exerted forces. (a) Draw a free-body diagram for the vessel. Assume no friction or drag forces affect the vessel. (b) Did you include all forces in the overhead view in your free-body diagram? Why or why non?

Figure shows the top view of two tugboats pulling a disabled vessel to the left. Arrow F1 is along the line connecting the vessel to the top tugboat. Arrow F2 is along the line connecting the vessel to the bottom tugboat. F1 is longer than F2. Arrow F subscript R shows the combined force. It is in between F1 and F2, pointing left and slightly up.

A ten.0-kg object is initially moving east at 15.0 m/s. And then a force acts on information technology for 2.00 due south, after which it moves northwest, also at xv.0 m/s. What are the magnitude and direction of the boilerplate strength that acted on the object over the 2.00-south interval?

On June 25, 1983, shot-doodle Udo Beyer of East Deutschland threw the 7.26-kg shot 22.22 m, which at that time was a world record. (a) If the shot was released at a height of 2.20 m with a project angle of [latex] 45.0\text{°} [/latex], what was its initial velocity? (b) If while in Beyer's manus the shot was accelerated uniformly over a distance of i.20 yard, what was the net force on it?

a. 14.1 m/southward; b. 601 North

A body of mass thou moves in a horizontal direction such that at time t its position is given by [latex] ten(t)=a{t}^{iv}+b{t}^{3}+ct, [/latex] where a, b, and c are constants. (a) What is the acceleration of the torso? (b) What is the fourth dimension-dependent force acting on the body?

A body of mass grand has initial velocity [latex] {5}_{0} [/latex] in the positive x-management. Information technology is acted on by a constant force F for fourth dimension t until the velocity becomes zippo; the force continues to human activity on the body until its velocity becomes [latex] \text{−}{5}_{0} [/latex] in the same amount of time. Write an expression for the total altitude the body travels in terms of the variables indicated.

[latex] \frac{F}{m}{t}^{ii} [/latex]

The velocities of a 3.0-kg object at [latex] t=6.0\,\text{s} [/latex] and [latex] t=viii.0\,\text{s} [/latex] are [latex] (3.0\hat{i}-vi.0\chapeau{j}+4.0\hat{grand})\,\text{1000/s} [/latex] and [latex] (-2.0\hat{i}+4.0\hat{k})\,\text{m/s} [/latex], respectively. If the object is moving at abiding dispatch, what is the force acting on information technology?

A 120-kg astronaut is riding in a rocket sled that is sliding along an inclined plane. The sled has a horizontal component of acceleration of [latex] five.0\,\text{1000}\text{/}{\text{south}}^{2} [/latex] and a downward component of [latex] 3.8\,\text{m}\text{/}{\text{s}}^{two} [/latex]. Calculate the magnitude of the force on the passenger past the sled. (Hint: Remember that gravitational acceleration must exist considered.)

2 forces are acting on a v.0-kg object that moves with acceleration [latex] 2.0\,{\text{m/southward}}^{ii} [/latex] in the positive y-direction. If one of the forces acts in the positive x-management and has magnitude of 12 N, what is the magnitude of the other force?

Suppose that you are viewing a soccer game from a helicopter in a higher place the playing field. Two soccer players simultaneously kick a stationary soccer ball on the apartment field; the soccer ball has mass 0.420 kg. The first player kicks with force 162 Northward at [latex] 9.0\text{°} [/latex] n of west. At the same instant, the 2nd actor kicks with force 215 N at [latex] xv\text{°} [/latex] e of south. Find the acceleration of the brawl in [latex] \chapeau{i} [/latex] and [latex] \chapeau{j} [/latex] form.

[latex] [/latex][latex] \overset{\to }{a}=-248\hat{i}-433\hat{j}\text{g}\text{/}{\text{s}}^{2} [/latex]

A ten.0-kg mass hangs from a spring that has the spring constant 535 Due north/m. Discover the position of the terminate of the spring away from its rest position. (Employ [latex] g=9.eighty\,{\text{m/s}}^{ii} [/latex].)

A 0.0502-kg pair of fuzzy dice is attached to the rearview mirror of a car past a short string. The automobile accelerates at constant rate, and the die hang at an angle of [latex] 3.20\text{°} [/latex] from the vertical because of the car's acceleration. What is the magnitude of the dispatch of the car?

[latex] 0.548\,{\text{grand/s}}^{2} [/latex]

At a circus, a donkey pulls on a sled carrying a small clown with a forcefulness given by [latex] 2.48\hat{i}+4.33\hat{j}\,\text{N} [/latex]. A horse pulls on the same sled, aiding the hapless donkey, with a strength of [latex] 6.56\hat{i}+5.33\hat{j}\,\text{Due north} [/latex]. The mass of the sled is 575 kg. Using [latex] \hat{i} [/latex] and [latex] \lid{j} [/latex] class for the answer to each problem, detect (a) the net force on the sled when the two animals human activity together, (b) the acceleration of the sled, and (c) the velocity afterward 6.50 south.

Hanging from the ceiling over a baby bed, well out of babe's reach, is a cord with plastic shapes, every bit shown hither. The string is taut (there is no slack), as shown by the straight segments. Each plastic shape has the same mass yard, and they are equally spaced by a distance d, as shown. The angles labeled [latex] \theta [/latex] describe the bending formed by the end of the string and the ceiling at each end. The heart length of sting is horizontal. The remaining two segments each class an angle with the horizontal, labeled [latex] \varphi [/latex]. Permit [latex] {T}_{1} [/latex] be the tension in the leftmost section of the string, [latex] {T}_{two} [/latex] be the tension in the section adjacent to it, and [latex] {T}_{3} [/latex] be the tension in the horizontal segment. (a) Find an equation for the tension in each section of the string in terms of the variables m, g, and [latex] \theta [/latex]. (b) Find the angle [latex] \varphi [/latex] in terms of the angle [latex] \theta [/latex]. (c) If [latex] \theta =5.10\text{°} [/latex], what is the value of [latex] \varphi [/latex]? (d) Observe the distance ten betwixt the endpoints in terms of d and [latex] \theta [/latex].

Figure shows four shapes hanging on a string that is attached to the ceiling at both ends. The shapes divide the string in five equal segments, each having length d. The middle segment is horizontal. The distance between the two ends of the string is x. The angles between the ceiling and the segments closest to the ceiling are both labeled theta. The angles formed by the first segments from the ceiling with their adjoining segments are both labeled phi.

a. [latex] {T}_{one}=\frac{2mg}{\text{sin}\,\theta } [/latex], [latex] {T}_{2}=\frac{mg}{\text{sin}(\text{arctan}(\frac{1}{two}\text{tan}\,\theta ))} [/latex], [latex] {T}_{3}=\frac{2mg}{\text{tan}\,\theta }; [/latex] b. [latex] \varphi =\text{arctan}(\frac{1}{2}\text{tan}\,\theta ) [/latex]; c. [latex] ii.56\text{°} [/latex]; (d) [latex] x=d(2\,\text{cos}\,\theta +two\,\text{cos}(\text{arctan}(\frac{1}{2}\text{tan}\,\theta ))+one) [/latex]

A bullet shot from a burglarize has mass of 10.0 g and travels to the right at 350 thou/s. It strikes a target, a large bag of sand, penetrating it a distance of 34.0 cm. Detect the magnitude and direction of the retarding force that slows and stops the bullet.

An object is acted on by three simultaneous forces: [latex] {\overset{\to }{F}}_{one}=(-three.00\hat{i}+2.00\lid{j})\,\text{N} [/latex], [latex] {\overset{\to }{F}}_{2}=(6.00\hat{i}-4.00\hat{j})\,\text{North} [/latex], and [latex] {\overset{\to }{F}}_{three}=(2.00\hat{i}+v.00\lid{j})\,\text{N} [/latex]. The object experiences dispatch of [latex] 4.23\,{\text{m/due south}}^{2} [/latex]. (a) Find the acceleration vector in terms of m. (b) Find the mass of the object. (c) If the object begins from rest, find its speed later five.00 s. (d) Find the components of the velocity of the object after 5.00 s.

a. [latex] \overset{\to }{a}=(\frac{v.00}{m}\hat{i}+\frac{three.00}{grand}\hat{j})\,\text{m}\text{/}{\text{s}}^{ii}; [/latex] b. 1.38 kg; c. 21.2 chiliad/s; d. [latex] \overset{\to }{v}=(18.1\hat{i}+ten.nine\hat{j})\,\text{m}\text{/}{\text{s}}^{two} [/latex]

In a particle accelerator, a proton has mass [latex] one.67\,×\,{10}^{-27}\,\text{kg} [/latex] and an initial speed of [latex] 2.00\,×\,{x}^{5}\,\text{thousand}\text{/}\text{due south.} [/latex] It moves in a straight line, and its speed increases to [latex] 9.00\,×\,{x}^{five}\,\text{1000}\text{/}\text{s} [/latex] in a altitude of 10.0 cm. Assume that the acceleration is constant. Find the magnitude of the force exerted on the proton.

A drone is being directed across a frictionless ice-covered lake. The mass of the drone is one.50 kg, and its velocity is [latex] 3.00\hat{i}\text{m}\text{/}\text{southward} [/latex]. After 10.0 s, the velocity is [latex] 9.00\chapeau{i}+4.00\hat{j}\text{g}\text{/}\text{southward} [/latex]. If a constant strength in the horizontal management is causing this change in motility, discover (a) the components of the force and (b) the magnitude of the force.

a. [latex] 0.900\chapeau{i}+0.600\hat{j}\,\text{N} [/latex]; b. 1.08 N

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Source: https://courses.lumenlearning.com/suny-osuniversityphysics/chapter/5-7-drawing-free-body-diagrams/

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