A pitcher throws a softball toward home plate. When the ball hits the catcher’s mitt, its horizontal velocity is 32 meters/second. The softball’s velocity goes to 0 meters/second in 0.8 seconds when caught. If the softball has a mass of 0.2 kilograms, what’s the force of the impact? Use F = ma, where . The force of the impact is newtons.
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Answer:
To calculate the force of impact F, first lets calculate the acceleration a of the ball:
a=v/t where v is the velocity of the ball and t is time
a=32/0.8=40 m/s2
To get the force F we need the Newtons second law:
F=m*a where m is the mass of the ball and a is the acceleration.
F=m*a = 0.2*40 = 8 N
So the impact force is F = 8 N.
Explanation:
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Concept:
- Force
- Calculating the change in momentum
- Expressing force as the rate of change of momentum
Given:
- The initial velocity of the softball u = 32 m/s
- The final velocity of the softball v = 0 m/s
- Time of impact t = 0.8
- Mass of the softball = 0.2 kg
Find:
- The force of the impact of the softball
Solution:
Force = Mass * acceleration
F = ma
v = u +at
0 = 32 + a (0.8)
a = -32/0.8
a = -40 m/s
F = ma
F= 0.2 (40) = 8 N
Or F = rate of change of momentum
F = Final momentum-initial momentum / time
Final momentum = mv = 0.2 (0) = 0
Initial momentum = mu = 0.2 (32) = 6.4
Time = 0.8s
F = 0-6.4/0.8 = -8 N
The force of the impact is 8 N.
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