A football punter accelerates a football from rest to a speed of 10 m/s during the time in which his toe is in contact with the ball (about 0.16 s). If the football has a mass of 0.50 kg, what average force does the punter exert on the ball?
To find the average force exerted by the punter on the ball, we can use Newton's second law of motion, which states that force is equal to the mass of an object multiplied by its acceleration:
Force = mass * acceleration
First, we need to find the acceleration of the football. We can use the formula:
Acceleration = (final velocity - initial velocity) / time
Given that the initial velocity (u) is 0 m/s, the final velocity (v) is 10 m/s, and the time (t) is 0.16 s, we can substitute these values into the formula:
Acceleration = (10 m/s - 0 m/s) / 0.16 s
Acceleration = 10 m/s / 0.16 s
Acceleration = 62.5 m/s^2
Now we have the acceleration of the football. Next, we can calculate the force exerted by the punter using Newton's second law. The mass of the ball is given as 0.50 kg:
Force = mass * acceleration
Force = 0.50 kg * 62.5 m/s^2
Force = 31.25 N
Therefore, the punter exerts an average force of 31.25 N on the ball.
To find the average force exerted by the punter on the ball, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). Rearranging the equation, we get:
F = m * a
First, we need to find the acceleration of the football. We know that the initial velocity (u) is 0 m/s, the final velocity (v) is 10 m/s, and the time (t) is 0.16 s. We can use the equation:
v = u + at
Solving for acceleration, we get:
a = (v - u) / t
Substituting the given values, we get:
a = (10 m/s - 0 m/s) / 0.16 s
a = 10 m/s / 0.16 s
a ≈ 62.5 m/s^2
Now we can calculate the average force exerted by the punter. Substituting the mass (m) and acceleration (a) values into the equation:
F = 0.50 kg * 62.5 m/s^2
F = 31.25 N
Therefore, the average force exerted by the punter on the ball is approximately 31.25 Newtons.