# Week 18

Reading: PSE Chap 13 ( Simple harmonic motion) and 16, waves
Some fascinating resources:

Homework Problems:
Just for practice for the final exam on Friday, Dec. 23.

1. Ice cube: A large ice cube, whose density is 0.917 g/cc, is placed in a glass. Water is then poured into the glass until the glass is full to the rim.
• First, what fraction of the ice cube is submerged? (Solution: 91.7 percent)
• When the ice melts, will the water level overflow the glass, will it fall below the rim, or will it remain the same? Explain your answer. (Solution: it would remain at the same level. Suppose the ice cube had a volume of 1 cc. 0.917 cc was below water. When it melts, the new volume will be 0.917 cc, since its density increased by just this much.)
2. Hydraulics: A fluid-filled syringe has a plunger with a diameter of 1 cm. The needle has a diameter of 1 mm. The plunger is depressed at a rate of 1 cm per second.
• With what speed will the fluid squirt from the tip of the needle? (Since the cross-sectional area of the needle is 1/100 that of the plunger, the speed will be 100 times as great. So the fluid squirts out at 100 cm/second.)
• If the end of the needle is capped, and a force of 1 pound is applied to the plunger, what force will be applied to the end cap? Explain your answer. (By pascal's principle, the force will be 1/100 of a pound)
3. Mass on a spring: A block of mass M = 1 kg is placed on a frictionless table. It is attached to a spring whose spring constant is 5 N/meter. The spring is compressed by 5 cm and then released at time t = 0.
• What is the angular frequency of the mass as it oscillates back and forth across the surface of the table? (omega = sqrt(5) rad/sec)
• Write down a mathematical function that describes the motion of the mass as a function of time. (x = 5cm * cos(omega * t))
• Make a plot of this function and label your axes appropriately.
• What are the kinetic energy and potential energies of the mass-spring system at t = 1 second.
• Wha tis the total energy of the mass-spring system while it is oscillating? (E = 2/160 joules)
General College Physics