A ball on a string spins in a horizontal circle of radius 2.5 m with a speed of 3.0 m/s. The tension in the string is 5.4 N. What is the mass of the ball?
Question
A ball on a string spins in a horizontal circle of radius 2.5 m with a speed of 3.0 m/s. The tension in the string is 5.4 N. What is the mass of the ball?
Solution
To solve this problem, we need to use the formula for centripetal force, which is F = mv^2/r, where m is the mass of the object, v is the velocity, and r is the radius of the circle.
In this case, the tension in the string is providing the centripetal force that keeps the ball moving in a circle. So we can set the tension equal to the centripetal force:
5.4 N = m * (3.0 m/s)^2 / 2.5 m
Solving for m gives us:
m = 5.4 N * 2.5 m / (3.0 m/s)^2
m = 1.5 kg
So the mass of the ball is 1.5 kg.
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