1. A 5.0-kg mass is attached to a spring and executes simple harmonic motion with a period of 2.0 s. If the total energy of the system is 10 J, what is the amplitude of the motion? [Hint: Start by finding k.] 2. A pendulum clock that ticks once per second (that being the period of one com- plete cycle of the pendulum) is taken to the moon to use as a timekeeper for a lunar colony. What will be the period of the pendulum when it is on the moon? [Hint: Remember that the gravitational field on the moon is 1/6 the strength of the gravitational field on the earth.] 3. A simple harmonic motion of a spring is described by the following graph x [m] 2 1 -1 -2 t [s] 2 3 4 (a) Reading from the graph, what is the period of this simple harmonic motion (no need to show steps)? (b) What is the frequency of this simple harmonic motion? (c) The simple harmonic motion can be written in the format of x = A cos (wt), find A and . (d) If this simple harmonic motion comes from an object attached with a spring that has a spring constant of 10 N/m, what is the mass of the object? 4. A diver experiences a doubling of the pressure by descending about 10.3 meters in fresh water (Patm = 101,000 Pa). How deep must you dive in a lake of alcohol (p = 790 kg/m) to achieve a doubling of the pressure? (Use g = 9.8 m/s here.) 5. An auto mechanic wants to raise a 10,000 kg truck on a hydraulic lift in which the large main cylinder has a radius of 10 cm. He uses compressed air to drive the small cylinder, as shown. What must the pressure of the compressed air be? How many atmospheres of pressure is this? Compressor 10 cm radius 6. A ball of mass 400 g and a volume 100 cm is released from rest just under the surface of a lake of fresh water. a) Find the buoyant force acting on the ball. [Hint: Be careful with units. To find a weight in newtons, you must use SI units for g (10 m/s) and for the mass.] b) Find the acceleration of the ball right after it has been released. 7. A cube of ice floats in a glass of fresh water with 90% of its volume below the surface (Pwater 1 g/cm). How much of the cube would be below the surface if it was put into a glass of alcohol instead (Palcohol = 0.8 g/cm)?