Question

# Consider the following scenario. You find yourself having some books with a total mass of 32...

Consider the following scenario. You find yourself having some books with a total mass of 32 kg that you have to move from your bedroom to the door of your apartment using a rope attached to the crate. The coefficient of static friction between the crate and the floor is 0.65, and the coefficient of kinetic friction is 0.45 .

(a) Pulling the rope horizontally, what is the minimum force you have to pull with to get the crate to start moving?

(b) Once the crate is moving, what is the force you have to pull with (with the rope horizontal) to keep the crate moving with constant velocity?

(c) Pulling the crate is hard work, so you stop to rest and decide to try something different: you hold the rope higher so that it angles upward from the crate, 30 degrees above horizontal. After pulling hard briefly to get the crate started, you ease up and pull just hard enough to keep it moving with constant velocity, holding the rope at that 30° angle. Draw a free-body diagram showing all the forces acting on the crate, including the (not yet determined) tension force T in the rope that you’re pulling on.

(d) Pulling at that angle, how many newtons of force do you have to pull with to keep the crate moving with constant velocity? (Hint: the normal force from the floor is not the same as it was in parts a and b, because the rope is now providing some force in the vertical direction.)

(e) Is your answer for part d less than, equal to, or greater than what you needed when pulling horizontally to keep it moving (part b)? So, is there some benefit from pulling at an angle?

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