To solve this problem, we need to use the formula for the tension in a string, which is given by T = m * ω² * r, where m is the mass of the ball, ω is the angular velocity, and r is the radius of the circle.

Step 1: Convert the frequency to angular velocity. The relationship between frequency (f) and angular velocity (ω) is ω = 2πf. So, ω = 2π * 25 Hz = 50π rad/s.

Step 2: Substitute the values into the tension formula. The radius (r) is the length of the string, which is 1.2 m. So, T = 0.22 kg * (50π rad/s)² * 1.2 m.

Step 3: Calculate the tension. T = 0.22 kg * (2500π² rad²/s²) * 1.2 m = 2073.4 N.

So, the tension in the string is approximately 2073.4 N.

Question

To solve this problem, we need to use the formula for the tension in a string, which is given by T = m * ω² * r, where m is the mass of the ball, ω is the angular velocity, and r is the radius of the circle.

Step 1: Convert the frequency to angular velocity. The relationship between frequency (f) and angular velocity (ω) is ω = 2πf. So, ω = 2π * 25 Hz = 50π rad/s.

Step 2: Substitute the values into the tension formula. The radius (r) is the length of the string, which is 1.2 m. So, T = 0.22 kg * (50π rad/s)² * 1.2 m.

Step 3: Calculate the tension. T = 0.22 kg * (2500π² rad²/s²) * 1.2 m = 2073.4 N.

So, the tension in the string is approximately 2073.4 N.

Knowee AI · Accepted Answer

To solve this problem, we need to use the formula for the tension in a string, which is given by T = m * ω² * r, where m is the mass of the ball, ω is the angular velocity, and r is the radius of the circle.

Step 1: Convert the frequency to angular velocity. The relationship between frequency (f) and angular velocity (ω) is ω = 2πf. So, ω = 2π * 25 Hz = 50π rad/s.

Step 2: Substitute the values into the tension formula. The radius (r) is the length of the string, which is 1.2 m. So, T = 0.22 kg * (50π rad/s)² * 1.2 m.

Step 3: Calculate the tension. T = 0.22 kg * (2500π² rad²/s²) * 1.2 m = 2073.4 N.

So, the tension in the string is approximately 2073.4 N.

A 0.22 kg ball is going in circles at a frequency of 25 Hz due to being attached to a 1.2 m long string. What is the tension in the string?

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