Question

2. Two students want to raise a heavy box onto the back of a truck. They do this by putting a rope through a handle on the box, and each lifting one side of the rope, as sketched. The arrangement is symmetrical, so that the rope makes an angle ? with the horizontal on either side. The box is moved at a constant speed. In this problem you will compute the magnitude of the tension in the rope. Let the mass of the trunk (including the handle) be M, and neglect the mass of the rope. a) Draw a free body diagram of the forces on the handle beside the "real world" picture below. b) Choose a sensible coordinate system, and write each of the forces as vectors in component form. c) Write down the horizontal and vertical components of F = ma. Use these equations to solve for the magnitude of the tension in each side of the rope. Give your final answer in terms of M, g, and ?. d) In this part suppose that while the two people are raising the box, they move it upward with a constant acceleration a. What is the magnitude of the tension in each rope now? Give your final answer in terms of M, g, a, and ?.

          2. Two students want to raise a heavy box onto the back of a truck. They do this by putting a
rope through a handle on the box, and each lifting one side of the rope, as sketched. The
arrangement is symmetrical, so that the rope makes an angle ? with the horizontal on either
side. The box is moved at a constant speed.

In this problem you will compute the magnitude of the tension in the rope. Let the mass of the
trunk (including the handle) be M, and neglect the mass of the rope.

a) Draw a free body diagram of the forces on the handle beside the "real world" picture
below.

b) Choose a sensible coordinate system, and write each of the forces as vectors in component
form.

c) Write down the horizontal and vertical components of F = ma. Use these equations to
solve for the magnitude of the tension in each side of the rope. Give your final answer in
terms of M, g, and ?.

d) In this part suppose that while the two people are raising the box, they move it upward with
a constant acceleration a. What is the magnitude of the tension in each rope now? Give
your final answer in terms of M, g, a, and ?.

Show more…

2. Two students want to raise a heavy box onto the back of a truck. They do this by putting a
rope through a handle on the box, and each lifting one side of the rope, as sketched. The
arrangement is symmetrical, so that the rope makes an angle ? with the horizontal on either
side. The box is moved at a constant speed.

In this problem you will compute the magnitude of the tension in the rope. Let the mass of the
trunk (including the handle) be M, and neglect the mass of the rope.

a) Draw a free body diagram of the forces on the handle beside the "real world" picture
below.

b) Choose a sensible coordinate system, and write each of the forces as vectors in component
form.

c) Write down the horizontal and vertical components of F = ma. Use these equations to
solve for the magnitude of the tension in each side of the rope. Give your final answer in
terms of M, g, and ?.

d) In this part suppose that while the two people are raising the box, they move it upward with
a constant acceleration a. What is the magnitude of the tension in each rope now? Give
your final answer in terms of M, g, a, and ?.

Added by Matthew C.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Thanks for your feedback!

Two students want to raise a heavy box onto the back of a truck. They do this by putting a rope through a handle on the box, and each lifting one side of the rope, as sketched. The arrangement is symmetrical, so that the rope makes an angle φ with the horizontal on either side. The box is moved at a constant speed. In this problem you will compute the magnitude of the tension in the rope. Let the mass of the trunk (including the handle) be M, and neglect the mass of the rope. a) Draw a free body diagram of the forces on the handle beside the "real world" picture below. b) Choose a sensible coordinate system, and write each of the forces as vectors in component form. c) Write down the horizontal and vertical components of F = ma. Use these equations to solve for the magnitude of the tension in each side of the rope. Give your final answer in terms of M, g, and φ. d) In this part suppose that while the two people are raising the box, they move it upward with a constant acceleration a. What is the magnitude of the tension in each rope now? Give your final answer in terms of M, g, a, and φ.

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Transcript

00:01 Hello.

00:02 So in the first question, we are asked to find, sorry, draw the free body diagram of the scenario.

00:09 Okay.

00:09 So this is the mass m and these are the angles 5.

00:14 Now let the tension acting on both these strings be t.

00:20 Okay.

00:20 Then each of these can be resolved into their horizontal as well as vertical components.

00:27 Now if we look at this diagram here, there is a tension t.

00:31 Acting in this direction at five angles to the horizontal.

00:37 Okay, then it can be resolved into two components.

00:41 The horizontal component, that is the t cosine 5 component and the vertical component, that is the t sine 5 component, okay, which is acting in the upward direction.

00:53 Now, coming to this tension here, it can also be resolved into two components, that is t cosine 5 which is acting in the negative x direction and then t sign 5 which is acting in the positive y direction.

01:07 Now we can see that here the vertical components of both the tension here act along the same line and hence we can mark it as 2t sine 5.

01:19 Then there is the weight of the body which is acting in the downward direction.

01:24 This is the free body diagram.

01:27 For the second question we have taken the horizontal.

01:30 Direction as the x -axis and the vertical direction as the y -axis now we have the tension t acting like this on both sides of the axis about the origin okay now these both these tensions make an angle of phi with the x -axis now this tension can be resolved into two components t -cosine -5 which is acting along the positive x -axis and t -sign -5 which is acting along the positive y -axis and here also the tension can be resolved into two components, t cosine 5 which is acting along the negative x axis and the t sine 5 which is acting along the positive y axis.

02:12 And both these vertical components add up to give 2 t sine 5 along the positive y axis.

02:18 Now there is the weight of the body, mg acting in the downward direction that is along the negative y axis...

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