Learning Goal: To use the principle of linear impulse and momentum to relate a force on an object to the resulting velocity of the object at different times. The equation of motion for a particle of mass m can be written as ∑F=ma=mdvdt By rearranging the terms and integrating, this equation becomes the principle of linear impulse and momentum: ∑∫t2t1Fdt=m∫v2v1dv=mv2−mv1 For problem-solving purposes, this principle is often rewritten as mv1+∑∫t2t1Fdt=mv2 The integral ∫Fdt is called the linear impulse, I, and the vector mv is called the particle's linear momentum. A tennis racket hits a tennis ball with a force of F=at−bt2, where a = 1300 N/ms , b = 300 N/ms2 , and t is the time (in milliseconds). The ball is in contact with the racket for 2.90 ms . If the tennis ball has a mass of 59.7 g , what is the resulting velocity of the ball, v, after the ball is hit by the racket?
Learning Goal:
To use the principle of linear impulse and momentum to relate a force on an object to the resulting velocity of the object at different times.
The equation of motion for a particle of mass m
can be written as
∑F=ma=mdvdt
By rearranging the terms and integrating, this equation becomes the principle of linear impulse and momentum:
∑∫t2t1Fdt=m∫v2v1dv=mv2−mv1
For problem-solving purposes, this principle is often rewritten as
mv1+∑∫t2t1Fdt=mv2
The integral ∫Fdt is called the linear impulse, I, and the
A tennis racket hits a tennis ball with a force of F=at−bt2, where a = 1300 N/ms , b = 300 N/ms2 , and t is the time (in milliseconds). The ball is in contact with the racket for 2.90 ms . If the tennis ball has a mass of 59.7 g , what is the resulting velocity of the ball, v, after the ball is hit by the racket?
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