Explaining Oscillatory Motion: Pendulums, Skateboards, and Grandfather Clocks

[ahrog]

Homework Statement

1. A screw is put into the top of a coconut and a long string is tied to the coconut so that it can be suspended to form a simple pendulum. A hole is then punched into the bottom of the coconut and the system is made to oscillate. The period of this pendulum is found to first increase and then decrease. Explain why this would happen.
2. A skateboarder stands at the top of a small gully. After supplying a small push, the skateboarder rolls down the side of the gully..Oscillatory motion occurs!
a) Explain why the oscillatory motion occurs.
b) The skateboarder stands at the top of a small hill. Explain why oscillatory motion does not occur in this case.
3. A grandfather clock uses a large mass suspended at the end of a metal rod as a timing mechanism. The back and forth movement of the mass provides the tick and tocks for this clock. An interesting characteristic of this type of clock is that it is sensitive to temperature. Imagine that 3 identical clocks are set to the same time, and then allowed to run for one week. These clocks are represented on the response page (just think of 2 blank circles and one clock showing 9:00) One clock (blank circle) ran in a room that was hot. The clock (blank circle) ran in a room that was cold. The clock (showing 9:00) ran in a room that was at room temp. Sketch the approx. times that the clocks in the hot and col rooms would show. Explain your answer.

Homework Equations

g=GM/R^2

The Attempt at a Solution

These questions are work about 20% of my module, so I would really appreciate help! Just telling me whether I'm right or wrong would help! Suggestions on what to add/take away would be really helpful too!

1. I'm not really sure why it matters that they drilled a hole in the bottom of the coconut. If someone finds the relevance (which there must be, please tell me!) This happens because the system is not perfect, it is a damped system. The air resistance works upon the coconut, causing it to slow down. This seems like a really short answer though, as it is worth 7 marks! I don't understand how to get seven marks out of this.

2. a) Oscillatory motion occurs because gravity is pulling the skateboarder down towards the center of the gully (lowest point). Because the skateboarder has wheels, which keep kinetic energy going, he will continue to move up the other side of the gully due to the restoring force. Again, the gravity will pull the skateboarder back towards equilibrium, and he will travel back down, and repeat the cycle. However, this motion will decrease over time, due to friction of the wheels, air resistance and gravity.
b) Oscillatory motion will not occur, because the skateboarder cannot repeat/reverse the path of rolling down the hill, without having another hill or something to roll back down. He cannot repeat the movement, and therefore, the movement is not oscillatory. For the skateboarder, there is no restoring force, which will move him in the opposite direction. Without this, he will roll in a straight line away from the hill, until coming to a stop.

3. I'm thinking that the pendulum would increase/decrease in length in cold/hot rooms, therefore moving faster/slower.

 

[Carid]

1. When you make a hole in a coconut you can pour out the milk.

3. You'd better make clear which one runs faster and which slower.

 

[ahrog]

Thank you, that helped a lot! I could now answer the questions, saying that the pendulum length increases and decreases as the milk drains out.

 

[Carid]

Losing the milk changes the centre of mass of the coconut and thus increases the effective length of the pendulum.