Links to answers and explanations are at the are at the end of the problem set.
1. An object of mass 0.5 kg is released from rest at a height H above the ground. It falls and hits the ground in 0.45 s. Show that H = 0.992 m. Find its initial potential energy and kinetic energy, and its total energy. (Potential energy is measured from the ground.) Find its velocity just before it hits the ground. Find its kinetic, potential, and total energy, just before it hits the ground.
2. An object of mass 0.2 kg is released from rest at a height H above the ground. It falls and hits the ground in 0.557 s. Show that H = 1.52 m. Find its initial potential energy and kinetic energy and its total energy. (Potential energy is measured from the ground.) Find its velocity just before it hits the ground. Find its kinetic, potential, and total energy, just before it hits the ground.
3. An object of mass = 1.2 kg is released from rest and falls for t = 0.2 s. Find the potential and kinetic energy, and the total energy, at the top point. (In this problem PE is measured from the bottom point.) Find the potential and kinetic energy, and the total energy, at the bottom point.
4. An object of mass = 0.4 kg is released from rest and falls for t = 0.3 s. Find the potential and kinetic energy, and the total energy, at the top point. (In this problem PE is measured from the bottom point.) Find the potential and kinetic energy, and the total energy, at the bottom point.
5. 100 g of water at 80 degrees is mixed with 100 g of water at 40 degrees. What is the final temperature? Verify that heat energy is conserved in this process.
6. 100 g of water at 70 degrees is mixed with 200 g of water at 40 degrees. The final temperature is 50 degrees. Verify that heat energy is conserved in this process.
7. 100 g of water at 20 degrees is mixed with 300 g of water at 60 degrees. The final temperature is 49 degrees. Show that heat energy is not conserved in this process. How much is lost to the environment?
8. 30 g of aluminum (c = 0.217) at 80 degrees is mixed with 200 g of water at 20 degrees. The final temperature is 21.89 degrees. Verify that heat energy is conserved in this process.
9. 30 g of copper (c = 0.093) at 80 degrees is mixed with 150 g of water at 22 degrees. The final temperature is 22.9 degrees. Show that heat energy is not conserved in this process. How much is lost to the environment?