A pendulum consisting of a ball of mass m is released from the position shown and strikes a block of mass M. The block slides a distance D before stopping under the action of steady friction force of 0.2 Mg.

m

M

L37

What is the speed of the pendulum ball just before it strikes the block?

If the pendulum ball rebounds to an angle of 20, what is the speed of the ball after the collision?

What is the speed of the block after the collision?

How far does the block move before coming to a stop?

A 26 kg boy is standing at rest on a 4 kg skateboard at the bottom of a frictionless hill as shown. A 5 kg ball comes at him with a horizontal velocity of 10 m/s to the right and he catches the ball and remains on the skateboard.

What is the speed of the boy the moment after he catches the ball?

How high up the hill does the boy coast if he momentarily comes to a rest.

After momentarily coming to rest, he begins to slide down the hill which is tilted with respect to the horizontal at an angle of 10. If the coefficient of kinetic friction is 0.1, what is his acceleration?

A 2.0 kg frictionless cart is moving at a constant speed of 3.0 m/s to the right on a horizontal surface, as shown above, when it collides with a second cart of undetermined mass m that is initially at rest. The force F of the collision as a function of time t is shown in the graph below, where t = 0 is the instant of initial contact. As a result of the collision, the second cart acquires a speed of 1.6 m/s to the right. Assume that friction is negligible before, during, and after the collision.

(a) Calculate the magnitude and direction of the velocity of the 2.0 kg cart after the collision. (b) Calculate the mass m of the second cart.

After the collision, the second cart eventually experiences a ramp, which it traverses with no frictional losses. The graph below shows the speed v of the second cart as a function of time t for the next 5.0 s, where t = 0 is the instant at which the carts separate.

(c) Calculate the acceleration of the cart at t = 3.0 s. (d) Calculate the distance traveled by the second cart during the 5.0 s interval after the collision (0 s < t < 5.0 s). 

(e) State whether the ramp goes up or down and calculate the maximum elevation (above or below the initial height) reached by the second cart on the ramp during the 5.0 s interval after the collision (0 s < t < 5.0 s).

An 80 kilogram person standing on a 20 kilogram ‑ ‑platform suspended by a rope passing over a stationary pulley that is free to rotate. The other end of the rope is held by the person. The masses of the rope and pulley are negligible. You may use g = 10 m/ s2. Assume that friction is negligible, and the parts of the rope shown remain vertical.a. If the platform and the person are at rest, what is the tension in the rope?

The person now pulls on the rope so that the acceleration of the person and the platform is 2 m/s2 upward.b. What is the tension in the rope under these new conditions?

c. Under these conditions, what is the force exerted by the platform on the person?