ISBN: 978-1133947271

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A 1.25-kg wooden block rests on a table over a large hole as in the figure. A 5.00-g bullet with an initial velocity v_{i} is fired upward into the bottom of the block and remains in the block after the collision. The block and bullet rise to a maximum height of 22.0 cm. Calculate the initial velocity of the bullet from the information provided.

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A cannon is rigidly attached to a carriage, which can move along horizontal rails but is connected to a post by a large spring, initially unstretched and with force constant k = 2.00 X 10^{4} N/m, as shown in the figure. The cannon fires a 200-kg projectile at a velocity of 125 m/s directed 45.0° above the horizontal. Assuming that the mass of the cannon and its carriage is 5000 kg,

(a) Find the recoil speed of the cannon.

(b) Determine the maximum extension of the spring.

(c) Find the maximum force the spring exerts on the carriage.

(d) Consider the system consisting of the cannon, carriage, and projectile. Is the momentum of this system conserved during the firing? Why or why not?

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A bullet of mass m = 8.00 g is fired into a block of mass M = 250 g that is initially at rest at the edge of a table of height h = 1.00 m. The bullet remains in the block, and after the impact the block lands d = 2.00 m from the bottom of the table. Determine the initial speed of the bullet.

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A 3.00-kg steel ball strikes a wall with a speed of 10.0 m/s at an angle of *θ* = 60.0° with the surface. It bounces off with the same speed and angle as shown in the figure. If the ball is in contact with the wall for 0.200 s, what is the average force exerted by the wall on the ball?

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A rod of length 30.0 cm has linear density (mass per length) given by λ = 50.0 + 20.0x where x is the distance from one end, measured in meters, and λ is in grams/meter.

(a) What is the mass of the rod?

(b) How far from the x = 0 end is its center of mass?

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