Assignment 2, solutions

Problem 1:

A 10 g bullet is stopped in a block of wood (m = 5 kg).  The speed of the bullet-wood combination immediately after the collision is 0.6 m/s.  What was the original speed of the bullet?

Solution:

Problem 2:

Moisture condenses at the constant rate λ units of mass per unit time on a falling raindrop.  If the drop falls from rest and has initial mass M, find the distance it has fallen in time t.  Neglect air resistance.

Solution:

Problem 3:

A chain of mass m and length L rests with (1 - α)L of its length on a table top and αL of its length hanging over the smooth edge, as shown in the following figure.

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(a)  The coefficient of friction of the tabletop is μ.  What is the maximum value, αc, for which the chain remains stationary?
(b)  If α is larger than αc, when released the chain will slide off the table.  What is the velocity of the chain when the last link leaves the table?

Solution:

Problem 4:

A 60 kg man standing fixed to the ground, can throw a m = 150 g baseball horizontally with a maximum speed of v0 = 25 m/s.
(a)  How much mechanical energy does he put into the throw?
(b)  Assume the man stands fixed to a 9.25 kg platform which moves frictionless with respect to the ground.  He has five 150 g baseballs and throws one of the baseballs horizontally as shown, putting in the same amount of mechanical energy as found in part (a).  The collision of the ball with the platform wall is elastic.  What is his velocity (magnitude and direction) after the throw?
image

(c)  What is the horizontal velocity component of the ball relative to the man?
(d)  Assume the man throws the remaining four balls sequentially, always putting in the same amount of mechanical energy.  What will be his final velocity?

Solution

Problem 5:

A flexible chain of length 3L and mass m hangs over a frictionless pulley so that the length of the vertical parts of the chain on either side of the pulley is L.  After a slight disturbance, the chain begins to slide to the right. What is the force exerted by the chain on the pulley at the instant the length of the vertical part of the chain on the right is 3L/2?
Hint:  What is the acceleration of the CM of the chain?

Solution