A child is twirling a 0.0116 kg ball on a string in a horizontal circle whose radius is 0.102 m. The ball travels once around the circle in 0.560 s.
(a) Determine the centripetal force acting on the ball.
N
(b) If the speed is doubled, does the centripetal force double?
yes
no
If not, by what factor does the centripetal force increase?
I was able to work the problem but i'm not sure what it means by factor for the third part of the problem. Please help.
To determine the answers to the questions, we need to use the formulas related to centripetal force and the relation between force and speed. Here's how you can solve it:
(a) To calculate the centripetal force acting on the ball, we can use the formula:
Centripetal force = (mass * velocity^2) / radius
The mass of the ball is given as 0.0116 kg, the radius is 0.102 m, and the velocity can be calculated as the circumference of the circle divided by the time taken to complete one rotation.
Circumference of the circle = 2 * π * radius
Velocity = Circumference / time
Substituting the given values into the formulas, we have:
Circumference = 2 * π * 0.102 m
Velocity = (2 * π * 0.102 m) / 0.560 s
Now, compute the velocity and substitute it into the centripetal force formula to calculate the force exerted on the ball.
(b) If the speed is doubled, does the centripetal force double? The answer is yes. According to the formula for centripetal force, increasing the velocity will directly result in an increase in the force.
If not, by what factor does the centripetal force increase? In this case, since the centripetal force is directly proportional to the square of the velocity, if the speed is doubled, the centripetal force will increase by a factor of 4.
To calculate the factor by which the centripetal force increases, you can divide the new force by the initial force:
Factor = New Centripetal force / Initial Centripetal force
Remember that the initial force was calculated in part (a) by substituting the values into the centripetal force formula.
I hope this explanation helps clarify the steps needed to solve the problem. If you have any further questions, please let me know!