A football punter accelerates a 0.54 kg foot-
ball from rest to a speed of 8.7 m/s in 0.24
s.
What constant force does the punter exert
on the ball?
Answer in units of N
To answer this question, we can use Newton's second law of motion, which states that the force exerted on an object is equal to the mass of the object multiplied by its acceleration. In this case, the object is the football, and we need to find the force exerted on it by the punter.
The given information is as follows:
Mass of the football (m) = 0.54 kg
Final velocity of the football (v) = 8.7 m/s
Time taken (t) = 0.24 s
We are given the initial velocity, but since the football starts from rest (initial velocity = 0), we can assume it in our calculations.
First, we need to calculate the acceleration of the football using the equation:
Acceleration (a) = Change in velocity / Time taken
a = (final velocity - initial velocity) / t
a = (8.7 m/s - 0 m/s) / 0.24 s
a = 36.25 m/s^2
Now that we have the acceleration, we can use Newton's second law to calculate the force exerted on the football:
Force (F) = mass (m) * acceleration (a)
F = 0.54 kg * 36.25 m/s^2
F = 19.61 N
Therefore, the punter exerts a constant force of 19.61 Newtons on the ball.
Impulse = Force * time = Momentum change
= Mass * (velocity change)
Solve for the force. The force does not have to be constant. I can be a time averaged force during contact