UCM physics helpp plz

Question

1. A runner completes 8 laps around a circular track in 480 s.

a. What is the period?

b. What is the frequency?

2. A pendulum completes one cycle in 0.2 s.

a. What is the frequency?

b. How much time will be required to complete 40 cycles?

3. An object is spun around in circular motion such that its frequency is 10.0 Hz.

a. What is the period of its rotation?

b. How much time will be required to complete 80 rotations?

Answer 1

For all of these it helps to know what the period and frequency represent. The period is the length of time of one cycle, and the frequency is the number of cycles in a unit of time. Frequency = 1/Period and period = 1/frequency

1. The period is the length of one cycle. Since the runner completes 8 laps in 480 s, we can divide 480 by 8 to find the length of one cycle. 480/8 = 60, so the period is 60 s. If you want the frequency in cycles per minute, it would be 1 since you complete one cycle in 60 seconds, or one minute. Frequency = 1 / period = 1/1 minute
2. If the pendulum completes one cycle in 0.2 seconds, that means that the period = 0.2 s. Then frequency = 1/period = 1/0.2 s = 5 per second. For the second part, we know one period is 0.2 s. To find how long 40 periods are, we multiply 0.2 by 40. So 0.2 x 40 = 8.
3. In this problem, we are given the frequency. Period = 1/frequency, so period = 1/10 hz = 0.1 s. If we want to find the time of 80 rotations, we just multiply 80 by the time of one rotation, or the period. So 80 x 0.1 s = 8 s.