Question

A boy uses a string to swing a 2 kg stone around his head. If the string can bear a maximum tension of 1,030 N, what is the maximum speed at which the boy can swing the stone without breaking the string?

a) 23.98 m/s
b) 32.54 m/s
c) 41.56 m/s
d) 51.83 m/s

Answer 1

To find the maximum speed at which the boy can swing the stone without breaking the string, we can use the equation T = m * v^2 / r, where T is the tension force, m is the mass of the stone, v is the velocity, and r is the length of the string. By rearranging the equation, we can solve for v and determine the maximum speed.

Step-by-step explanation:

To determine the maximum speed at which the boy can swing the stone without breaking the string, we need to consider the tension force experienced by the string.

Since the string can bear a maximum tension of 1,030 N, we can set up the equation:

1. Let T be the tension force in the string.
2. Since the stone is moving in a circle, the tension force provides the centripetal force required for circular motion.
3. The centripetal force (Fc) is given by Fc = m * a, where m is the mass of the stone and a is the centripetal acceleration.
4. Using the equation for centripetal acceleration a = v^2 / r, where v is the velocity of the stone and r is the radius of the circular motion (equal to the length of the string), we can substitute this into the equation for centripetal force to get Fc = m * v^2 / r.
5. Setting the tension force equal to the centripetal force, we have T = m * v^2 / r.
6. Substituting the given values of m = 2 kg, T = 1,030 N, and r = length of the string, we can solve for v.

By rearranging the equation, we get v = √(T * r / m).

Plugging in the given values, v = √(1,030 N * r / 2 kg).

Therefore, the maximum speed at which the boy can swing the stone without breaking the string is the square root of (1,030 N times the length of the string divided by 2 kg).