A child is twirling a 0.0100 kg ball on a string in a horizontal circle whose radius is 0.118 m. The ball travels once around the circle in 0.460 s.
(a) Determine the centripetal force acting on the ball.
(b) If the speed is doubled, does the centripetal force double? (yes or no)
If not, by what factor does the centripetal force increase?
speed of ball= 2PI*radius/time
a) force= mass*v^2/r
b) what happens when v doubles?
when v doubles it does the centripetal force does not increase by 2, but rather by 4.
To answer this question, we need to use the formula for centripetal force:
F = (m * v^2) / r
where:
F is the centripetal force
m is the mass of the object (0.0100 kg)
v is the velocity of the object
r is the radius of the circle (0.118 m)
To find the velocity, we can use the formula:
v = (2 * π * r) / T
where:
T is the time it takes for the ball to travel once around the circle (0.460 s)
π is approximately 3.14159
Let's calculate the values step by step:
Step 1: Calculate the velocity (v).
v = (2 * π * r) / T
= (2 * 3.14159 * 0.118) / 0.460
= 1.619 m/s
Step 2: Substitute the values into the formula for centripetal force (F).
F = (m * v^2) / r
= (0.0100 * 1.619^2) / 0.118
= 0.222 N
(a) Therefore, the centripetal force acting on the ball is 0.222 N.
(b) If the speed is doubled, does the centripetal force double?
No, doubling the speed does not double the centripetal force.
To find by what factor the centripetal force increases, let's consider the centripetal force formula:
F = (m * v^2) / r
If the speed is doubled, the new velocity would be 2v. Substituting this into the formula:
F' = (m * (2v)^2) / r
= (m * 4v^2) / r
= 4 * (m * v^2) / r
= 4F
Therefore, if the speed is doubled, the centripetal force increases by a factor of 4.