Q1- A girl pulls a box of mass **m = 6 kg** across a floor with a constant horizontal force **F = 35 N**. Initially the block is at rest. For the first **d _{1} = 7 m**, there is no friction between the box and the floor. For the next

**d**the coefficient of friction between the box and the floor is m

_{2}= 7 m**= 0.1**.

a) What is the work done on the box by the girl in moving the box over the distance **d _{1} + d_{2}**?

b) What is work done on the box by friction in moving the box over the distance **d _{1} + d_{2}**?

c) What is the final speed of the box (after being pushed to **d _{1} + d_{2}**)?

d) How high up will it go? (measured vertically from the floor)

Q2 - A bobsled run leads down a hill as sketched in the figure above. Between points A and D, friction is negligible. Between points D and E at the end of the run, the coefficient of kinetic friction is **0.5**. The mass of the bobsled with drivers is **250 kg** and it starts from rest at point A.

a) Find the speed of the bobsled at point B.

b) Find the work done by gravity on the sled between points A and C.

Q3 - The two problems below are related to a cart of mass **M = 500 kg** going around a circular loop-the-loop of radius **R = 10 m**, as shown in the figures. All surfaces are frictionless. In order for the cart to negotiate the loop safely, the normal force exerted by the track on the cart at the top of the loop must be at least equal to **0.4** times the weight of the cart. You may neglect the size of the cart. (Note: This is different from the conditions needed to "just negotiate" the loop.)

a) For this part, the cart slides down a frictionless track before encountering the loop. What is the minimum height **h** above the top of the loop that the cart can be released from rest in order that it safely negotiate the loop?

b) For this part, we launch the cart horizontally along a surface at the same height as the bottom of the loop by releasing it from rest from a compressed spring with spring constant **k = 10000 N/m**. What is the minimum amount **X** that the spring must be compressed in order that the cart "safely" (as defined above) negotiate the loop?

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IriamAbhigyan Martin Ninama