Problem 1: A man in a train station is towing his 20kg trunk by pulling on a strap at an angle θ above the horizontal. He pulls on the strap with a 35N force and the force of friction by the surface on the trunk is 20N. As a result, the trunk is moving at a constant speed.
(a) Draw a free body diagram.
(b) What angle does the strap make with the horizontal?
(c) What is the normal force exerted by the ground on the trunk?
Problem 2: For spring break, you travel back home to visit your parents. While trying to relax at their house, your dad makes you help him clean the garage. He asks you to move a 50kg box from one side of the garage to the other. The box is too awkward to carry, so you attach an old rope to the box so you can pull it across the floor. You pull the box at an angle of 30? and the static coefficient of friction between the box and the floor is 0.25.
(a) Draw a free body diagram for the box while you are pulling on the rope, but the box doesn’t move.
(b) If you pull the rope with a force of 100N at the same angle, does the box move? (Prove it)
(c) Because the rope has been in the garage for a very long time, it will break if it experiences a force greater than 150N. What is the minimum amount of force you need to pull to get the box moving? Is the rope strong enough to get the box moving if you pull at this same angle? (You may want to rethink your answer to b)
(d) Without cleaning the dirty garage floor, or otherwise introducing anything between the two surfaces, how could you decrease the force due to friction? Explain!
Problem 3: A crow flying at 2 m s in the horizontal direction (parallel to the flat ground) opens its beak to caw at another bird and accidentally drops a piece of bread he was carrying, from a height of 10m above the ground. The bread is released with no initial vertical velocity.
(a) How long does it take for the bread to hit the ground?
(b) How far does the bread travel horizontally before it lands?
(c) What is the velocity (both components, or magnitude and direction) of the bread just before it hits the ground?
(d) What is the speed of the bread just before it hits the ground?
Problem 4: Consider a block sliding down an inclined plane that makes an angle of 35? with the horizontal. Assume the coefficient of kinetic friction between the block and the incline is µk = 0.25.
(a) Draw a free-body diagram for the block.
(b) If the mass of the block is 2 kg, find the components of the gravitational force in the given coordinate system.
(c) Find the normal force and the force of kinetic friction.
(d) Find the magnitude of the acceleration of the block.
(e) What is the final speed of the block after sliding 0.75m?
(f) If the coefficient of static friction is µs = 0.4, what would the maximum value of the angle θ be for the block to not slide when it is released?
Problem 5: A man standing on the roof of a building thinks it might be fun to try and toss a brick that he has found there into a garbage truck that is coming down the road. The building is 100m high, and the top of the trash pile (which is uncovered) is 2m above the ground. The road is 30m from the building at closest approach. The truck is moving down the road with constant velocity 15m/s. The man chooses to throw the brick at an angle of 45? above the horizontal.
(a) With what initial speed does he need to throw the brick so that it hits the top of the trash pile when the truck is 30m away from the building? Does this sound feasible?
(b) How far down the road must the truck be when he throws the brick so that it is at its closest approach when the brick lands in the trash pile?
(c) What will be the velocity of the brick when it hits the trash pile?