Question

A 205 g ball is tied to a string. it is pulled to an angle of 4.80 ∘ and released to swing as a pendulum. a student with a stopwatch finds that 18 oscillations take 18.0 s . How long is the string?

Answer 1

To determine the length of the string of a simple pendulum, we use the period equation T = 2π√(L/g). The measured period is 1 second for one oscillation, and by rearranging the equation and inserting the values, we find that the length of the string is approximately 0.248 meters or 24.8 centimeters.

Step-by-step explanation:

To find the length of the string of a pendulum given the number of oscillations and the time they take, we utilize the formula of the period of a simple pendulum:

T = 2π √(L / g)

Where T is the period of one oscillation, L is the length of the string, and g is the acceleration due to gravity (approximately 9.81 m/s2 on Earth). Given that the student measured 18.0 seconds for 18 oscillations, the period T is 1 second per oscillation.

Using the formula T = 2π √(L / g), we can solve for L as follows:

1. First, square both sides of the equation: T2 = (4π2)(L / g)
2. Multiply both sides by g to get gT2 = 4π2L
3. Divide both sides by 4π2 to isolate L: L = (gT2) / (4π2)
4. Substitute the known values: L = (9.81 m/s2 × 1 s2) / (4π2)
5. Calculate the length L

Applying the values, we get L = (9.81 × 12) / (4 × 3.14162) ≈ 0.248 m.

Therefore, the length of the string is approximately 0.248 meters or 24.8 centimeters.