Physics Problems

A M\(_1\) = 5 kg box rests on a table and is connected to a second box of mass M\(_2\) = 10 kg via a rope that hangs over a frictionless pulley as shown. The coefficient of friction, \(\mu\) is 0.2, Use free body diagrams to answer the following:



A. What is the acceleration of the system?
B. What is the tension in the rope?

A M\(_1\) = 8 kg box rests on a table and is connected to a second box of mass M\(_2\) = 4 kg via a rope that hangs over a pulley as shown. The coefficient of static friction, \(\mu_s\) is 0.2, and the coefficient of kinetic friction \(\mu_k\) is 0.1. Use a free body diagrams to answer the following.



A. Is the 4 kg box massive enough to cause the system to move?

B. If the box does cause the system to move, what is the acceleration of the system, and the tension in the rope?

The large block m\(_1\) is 10 kg, and the smaller block m\(_2\) is 1 kg. The coefficient of kinetic friction is 0.1. Determine the acceleration of the system and the contact force between the blocks. The applied force, F is 30 N. Also draw a free body diagram for both blocks.

A ball of mass \(M\) is thrown vertically upward with an initial speed of \(v_0\). It experiences a force of air resistance given by \(F = -kv\), where \(k\) is a positive constant. The positive direction for all vector quantities is upward. Express all algebraic answers in terms of \(M\), \(k\), \(v_0\), and fundamental constants.

• Does the magnitude of the acceleration of the ball increase, decrease, or remain the same as the ball moves upward?
• Write, but do NOT solve, a differential equation for the instantaneous speed \(v\) of the ball in terms of time \(t\) as the ball moves upward.
• Determine the terminal speed of the ball as it moves downward.
• Does it take longer for the ball to rise to its maximum height or to fall from its maximal height back to the height from which it was thrown? Justify your answer.
• Sketch a graph of velocity versus time for the upward and downward parts of the ball's flight, where \(t_f\) is the time at which the ball returns to the height from which it was thrown.