A pendulum clock is accurate on earth, where the period of its pendulum is 1.00 s.
(a) Find its period on the moon, where gravitational acceleration is 1.6 m/s2.
(b) During a 2 h interval, what would be the elapsed time shown on the clock?
CAN YOU PLEASE PROVIDE AN ANSWER WITH WORK . THANK YOU
multiply the period by sqrt 6. Figure out why this works.
b. if the clock is slower by a factor of sqrt6, then it should be 2hr/sqrt6 hrs. Think about that.
Sure! Let's start with part (a):
(a) To find the period of the pendulum on the moon, we can use the equation:
T = 2π √(L/g)
Where T is the period of the pendulum, L is the length of the pendulum, and g is the gravitational acceleration.
On Earth, we are given that the period is 1.00 s, so we can use this information to find the length of the pendulum there. Let's assume the length of the pendulum on Earth is L1.
1.00 s = 2π √(L1/9.8 m/s^2)
Next, we can use the ratio of gravitational accelerations on the moon and Earth to find the length of the pendulum on the moon. Let's assume the length of the pendulum on the moon is L2.
1.6 m/s^2 / 9.8 m/s^2 = √(L2/L1)
Squaring both sides of the equation, we get:
(1.6 m/s^2 / 9.8 m/s^2)^2 = L2/L1
(0.1633)^2 = L2/L1
0.0267 = L2/L1
Now, we can substitute this value of L2/L1 into the equation we derived earlier for the period on the moon:
T = 2π √(L2/1.6 m/s^2)
T = 2π √(0.0267/1.6 m/s^2)
T ≈ 0.324 s
Therefore, the period of the pendulum on the moon is approximately 0.324 seconds.
Moving on to part (b):
(b) The elapsed time shown on the clock is determined by the number of periods that have passed. We can calculate the number of periods in a 2-hour interval and then multiply it by the period of the pendulum on the moon to get the total elapsed time.
Number of periods = 2-hour time interval / period on the moon
Let's convert the 2-hour time interval into seconds:
2 hours = 2 × 60 minutes/hour × 60 seconds/minute = 7200 seconds
Number of periods = 7200 seconds / 0.324 seconds = 22,222.22 (approximately)
So, the elapsed time shown on the clock during a 2-hour interval would be approximately 22,222.22 seconds.