A 0.140 kg baseball traveling 39.0 m/s strikes the catchers mitt, which, in bringing the ball to rest, recoils backward 13 cm. What is the average force applied by the ball on the glove?
Physics - drwls, Monday, June 11, 2012 at 1:24pm
Use this formula:
Force x distance = work done against mitt = Kinetic Energy change
Which leads to:
Force = (1/2)M V^2/d
If you want to start from F = m*a, you have to use an equation for the acceleration, a
a = V/t = v/[d/(v/2)] = v^2/(2d)
F = m*V^2/(2d)
To find the average force applied by the ball on the glove, we can use the impulse-momentum principle. The impulse (J) is the product of the force (F) and the time (t) over which the force is applied:
J = F * t
The impulse can also be calculated as the change in momentum (Δp) of the ball:
J = Δp
The change in momentum is given by:
Δp = mv - mu
Where m is the mass of the ball, v is the final velocity of the ball (which is 0 as it comes to rest), and u is the initial velocity of the ball.
In this case, the initial velocity of the ball (u) is 39.0 m/s and the final velocity (v) is 0.
The change in momentum can be expressed as:
Δp = m * (v - u)
Substituting the given values:
Δp = 0.140 kg * (0 - 39.0 m/s)
Δp = -5.46 kg·m/s
Since the ball is brought to rest by the glove, the change in momentum is equal to the impulse applied by the ball on the glove:
J = Δp = -5.46 kg·m/s
To calculate the average force (F), we divide the impulse by the time (t) over which the force is applied. The time can be determined by converting the displacement (13 cm) into meters and dividing by the initial velocity (39.0 m/s):
t = displacement / initial velocity
t = 0.13 m / 39.0 m/s
t = 0.00333 s
Substituting the values into the original equation:
F = J / t
F = (-5.46 kg·m/s) / (0.00333 s)
F = -1640.2 N
The average force applied by the ball on the glove is approximately 1640.2 Newtons in magnitude. The negative sign indicates that the force is in the opposite direction of the initial velocity of the ball.