An inquiring student that has a mass of 65.0 kg is watching a crane with a wrecking ball demolish a building next door. The wrecking ball is swinging parallel to the property fence between her house and the neighbor’s. In an effort to estimate the length of the cable on the wrecking ball the student fashions a pendulum from a rock and a string. Her pendulum turns out to be 0.500m long. She then observes that the wrecking ball completes one oscillation in the same amount of time that it takes the rock to complete 5 cycles. What is the length of the cable on the wrecking ball?

Question

An inquiring student that has a mass of 65.0 kg is watching a crane with a wrecking ball demolish a building next door. The wrecking ball is swinging parallel to the property fence between her house and the neighbor’s. In an effort to estimate the length of the cable on the wrecking ball the student fashions a pendulum from a rock and a string. Her pendulum turns out to be 0.500m long. She then observes that the wrecking ball completes one oscillation in the same amount of time that it takes the rock to complete 5 cycles. What is the length of the cable on the wrecking ball?

Answer 1

for rock:

T = 2 pi sqrt (L/g)
T = 2 pi sqrt (.5/g)

for ball Tb = 5 T
so
5 T = 2 pi sqrt (Lb/g)
===================

10pi sqrt (.5/g) = 2pi sqrt (Lb/g)

5 sqrt (.5) = sqrt(Lb)

25 (.5) = Lb

Lb = 12.5

Answer 2

To find the length of the cable on the wrecking ball, we can use the formula for the period of a simple pendulum:

T = 2π√(L/g)

Where:
T = period (time taken for one complete oscillation)
L = length of the pendulum
g = acceleration due to gravity (approximately 9.8 m/s²)

Given that the student's pendulum has a length of 0.500 m and the rock completes 5 cycles in the same time it takes the wrecking ball to complete one oscillation, we can calculate the period of the rock's oscillation.

The period of the rock's oscillation is equal to 5 times the period of the wrecking ball's oscillation, so:

T_rock = 5 * T_wrecking ball

Substituting this into the formula for the period of a pendulum, we get:

2π√(L_rock/g) = 5 * 2π√(L_wrecking ball/g)

The 2π cancels on both sides, leaving us with:

√(L_rock/g) = 5 √(L_wrecking ball/g)

Now, let's simplify this equation by squaring both sides:

(L_rock/g) = 25 * (L_wrecking ball/g)

Since the "g" terms cancel out, we are left with:

L_rock = 25 * L_wrecking ball

We know that the length of the rock's pendulum is 0.500 m, so we can substitute this value and solve for the length of the wrecking ball's cable:

0.500 m = 25 * L_wrecking ball

Dividing both sides by 25, we find:

L_wrecking ball = 0.500 m / 25

Therefore, the length of the cable on the wrecking ball is 0.020 m.

Please note that the mass of the student and the details of the crane and wrecking ball are not necessary to determine the length of the cable on the wrecking ball in this scenario.