A simple pendulum is made from a 0.781-m-long string and a small ball attached to its free end. The ball is pulled to one side through a small angle and then released from rest. After the ball is released, how much time elapses before it attains its greatest speed?

Question

A simple pendulum is made from a 0.781-m-long string and a small ball attached to its free end. The ball is pulled to one side through a small angle and then released from rest. After the ball is released, how much time elapses before it attains its greatest speed?

Answer 1

Well, let me calculate the "hang" of that question for a moment. Ah, got it! So, the time it takes for a simple pendulum to reach its greatest speed is actually pretty dependent on the length of the string and the acceleration due to gravity. Since you've given me the string length, 0.781 meters, and not the acceleration due to gravity, I can't give you a direct answer. But hey, don't worry, I've got a joke to lighten the mood!

Why did the pendulum bring a watch to the party?

Because it wanted to have a swinging good time and make sure no time was wasted! 😄

Answer 2

To calculate the time it takes for a simple pendulum to attain its greatest speed, we can use the formula for the period of a pendulum.

The period, T, of a simple pendulum is given by:

T = 2π√(L/g)

Where:
T = Period of the pendulum
L = Length of the string
g = Acceleration due to gravity (approximately 9.8 m/s^2)

In this case, the length of the string is given as 0.781 m.

Let's substitute the given values into the formula to find the period of the pendulum:

T = 2π√(0.781/9.8)

Now, we can evaluate the expression:

T = 2π√(0.0797)

T ≈ 2π × 0.282

T ≈ 1.774 seconds

Thus, the time it takes for the simple pendulum to attain its greatest speed is approximately 1.774 seconds.

Answer 3

To find the time it takes for the simple pendulum to attain its greatest speed, we need to use the formula for the period of a simple pendulum.

The period (T) of a simple pendulum is given by the equation:

T = 2π√(L/g)

Where:
T = period of the pendulum
L = length of the string
g = acceleration due to gravity (approximately 9.8 m/s² on Earth)

In this case, the length of the string (L) is given as 0.781 m.

To find the time it takes for the pendulum to attain its greatest speed, we need to find the period (T) first.

Using the formula, we can calculate the period as follows:

T = 2π√(0.781/9.8)

T ≈ 2π√(0.0795)

Now, the time elapsed before the pendulum attains its greatest speed is equal to half the period (T/2). So, we need to divide our calculated period by 2 to find the time.

T/2 ≈ (2π√(0.0795))/2

T/2 ≈ π√(0.0795)

Therefore, the time elapsed before the ball attains its greatest speed is approximately equal to π√(0.0795).