Question

A 2.6 kg mass attached to a light string rotates on a horizontal,

frictionless table. The radius of the circle is 0.525 m, and the
string can support a mass of 17.9 kg before breaking. The
acceleration of gravity is 9.8m/s2. What maximum speed can
the mass have before the string breaks?

Answer 1

To find the maximum speed the mass can have before the string breaks, use the formula for centripetal force. Consider the maximum tension the string can support and solve for the maximum speed.

Step-by-step explanation:

To find the maximum speed the mass can have before the string breaks, we need to consider the tension in the string. The tension provides the centripetal force that keeps the mass moving in a circle. We can use the formula for centripetal force, Fc = (m*v^2)/r, where Fc is the tension, m is the mass, v is the speed, and r is the radius of the circle.

When the string is at its maximum tension, it can support a mass of 17.9 kg. Substituting these values into the formula, we can solve for the maximum speed, v.

Using m = 17.9 kg, r = 0.525 m, and g = 9.8 m/s^2, we get:
Tension = (m * v^2) / r
17.9 * 9.8 = (17.9 * v^2) / 0.525
Solving for v, we find that the maximum speed the mass can have before the string breaks is approximately 5.35 m/s.