Chapter 6. Problems: Conservation of Energy and Momentum
In this set we solve problems, in which we have conservation of both energy and momentum.
Problem 1. A 5.0-kg box moves along a straight line with constant velocity of 4.0 m/s. It collides elastically with a stationary box of mass 10 kg. Find the velocities of two boxes after the perfectly elastic collision.
Problem 2. A block of mass 2 kg hangs by a string of length 1 m. A second block of mass 4 kg slides along a frictionless surface with velocity 10 m/s. How high the 2 kg block will rise after elastic collision between the blocks.
Problem 3. A horizontal massless spring with spring constant 600 N/m is compressed 20 cm. The spring launches a block of mass 2 kg across a frictionless surface. The block collides with a stationary block of mass 10 kg. After perfectly elastic collision between the blocks the 2 kg block bounces back and then hits the spring. Find the maximum compression of the spring.
Problem 4.
A 5.0 kg cart rolls across a horizontal frictionless surface at 10 m/s toward a stationary 2 kg cart. The 5.0 kg cart has a horizontal ideal spring with a spring constant 300 N/m attached to the cart's front. Find the maximum compression of the spring.
Problem 5. Two blocks are on a horizontal frictionless surface. They are connected by a rope as shown in the figure. An ideal spring with spring constant 200 N/m is placed between the blocks. The compression of the spring is 10 cm. After the rope is cut the spring launches the blocks across the surface. The masses of the blocks are 5 kg and 10 kg. Find the maximum speeds of the blocks.
Problem 6. A catapult standing on a frictionless surface is used to launch a ball of mass 5 kg. The launch velocity of the ball is 5 m/s and the launch angle is . The mass of the catapult is 20 kg. The launching element of the catapult is a spring. Find the energy stored in the spring. Disregard the energy loss during the launch.
. The mass of the catapult is 20 kg. The launching element of the catapult is a spring. Find the energy stored in the spring. Disregard the energy loss during the launch.