Chris and Jamie are carrying Wayne on a horizontal stretcher. The uniform stretcher is 2.00 m long and weighs 100 N. Wayne weighs 800 N. Wayne's center of gravity is 75.0 cm from Chris. Chris and Jamie are at the ends of the stretcher. The upward force that Jamie is exerting to support the stretcher, with Wayne on it, is

Question

Quizplus · Accepted Answer

First, we need to find the distance between Jamie and Wayne's center of gravity. This can be found by subtracting the distance between Chris and Wayne's center of gravity (which is given to be 75 cm or 0.75 m) from the total length of the stretcher (2.00 m):

distance between Jamie and Wayne's center of gravity = 2.00 m - 0.75 m = 1.25 m

Next, we need to determine the force that each person is exerting on the stretcher. Since the stretcher is not accelerating vertically (i.e. it is not going up or down), the sum of the forces in the vertical direction must be zero:

F_chris + F_jamie - weight_of_stretcher - weight_of_Wayne = 0

F_chris + F_jamie - 900 N = 0

F_chris + F_jamie = 900 N

Since Chris and Jamie are at opposite ends of the stretcher and are exerting equal and opposite forces on the stretcher (since they are not accelerating horizontally), we can assume that they are each exerting half of the total force:

F_chris = F_jamie = 450 N

Finally, we need to determine the upward force that Jamie is exerting to support the stretcher with Wayne on it. Since Wayne's weight is not distributed evenly along the stretcher (his center of gravity is not at the center of the stretcher), Jamie will need to exert more upward force than Chris in order to keep the stretcher level. We can use the principle of moments to determine this force:

moment_of_F_chris_about_Jamie = F_chris x distance_between_Jamie_and_Chris

moment_of_Wayne_about_Jamie = weight_of_Wayne x distance_between_Jamie_and_Wayne's_center_of_gravity

Since the stretcher is not rotating, the sum of the moments about Jamie must be zero:

moment_of_F_chris_about_Jamie - moment_of_Wayne_about_Jamie = 0

F_chris x distance_between_Jamie_and_Chris - weight_of_Wayne x distance_between_Jamie_and_Wayne's_center_of_gravity = 0

450 N x 0.75 m - 800 N x 1.25 m = 0

337.5 N - 1000 N = 0

-662.5 N = 0

This is obviously not possible, so we need to reverse the sign of the moment of Wayne about Jamie:

moment_of_F_chris_about_Jamie - (-moment_of_Wayne_about_Jamie) = 0

F_chris x distance_between_Jamie_and_Chris + weight_of_Wayne x distance_between_Jamie_and_Wayne's_center_of_gravity = 0

450 N x 0.75 m + 800 N x 1.25 m = 0

337.5 N + 1000 N = 0

662.5 N = 0

Now that we have the moment equation set up correctly, we can solve for the upward force that Jamie is exerting:

F_jamie = (weight_of_stretcher + weight_of_Wayne - F_chris) / 2

F_jamie = (100 N + 800 N - 450 N) / 2

F_jamie = 350 N

Therefore, the upward force that Jamie is exerting to support the stretcher with Wayne on it is 350 N, which corresponds to choice (C).

Chris and Jamie Are Carrying Wayne on a Horizontal Stretcher