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Professional Application
Suppose a child drives a bumper car head on into the side rail, which exerts a force of 4000 N on the car for 0.200 s. (a) What impulse is imparted by this force? (b) Find the final velocity of the bumper car if its initial velocity was 2.80 m/s and the car plus driver have a mass of 200 kg. You may neglect friction between the car and floor.
a) $\text{800 kg}\cdot \text{m/s}$ away from the wall
b) $1\text{.}\text{20 m/s}$ away from the wall
Professional Application
One hazard of space travel is debris left by previous missions. There are several thousand objects orbiting Earth that are large enough to be detected by radar, but there are far greater numbers of very small objects, such as flakes of paint. Calculate the force exerted by a 0.100-mg chip of paint that strikes a spacecraft window at a relative speed of $4\text{.}\text{00}\times {\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{m/s}$ , given the collision lasts $6\text{.}\text{00}\times {\text{10}}^{\u20138}\phantom{\rule{0.25em}{0ex}}\mathrm{s}$ .
Professional Application
A 75.0-kg person is riding in a car moving at 20.0 m/s when the car runs into a bridge abutment. (a) Calculate the average force on the person if he is stopped by a padded dashboard that compresses an average of 1.00 cm. (b) Calculate the average force on the person if he is stopped by an air bag that compresses an average of 15.0 cm.
(a) $1\text{.}\text{50}\times {\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\mathrm{N}$ away from the dashboard
(b) $1\text{.}\text{00}\times {\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}\mathrm{N}$ away from the dashboard
Professional Application
Military rifles have a mechanism for reducing the recoil forces of the gun on the person firing it. An internal part recoils over a relatively large distance and is stopped by damping mechanisms in the gun. The larger distance reduces the average force needed to stop the internal part. (a) Calculate the recoil velocity of a 1.00-kg plunger that directly interacts with a 0.0200-kg bullet fired at 600 m/s from the gun. (b) If this part is stopped over a distance of 20.0 cm, what average force is exerted upon it by the gun? (c) Compare this to the force exerted on the gun if the bullet is accelerated to its velocity in 10.0 ms (milliseconds).
A cruise ship with a mass of $1\text{.}\text{00}\times {\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}\text{kg}$ strikes a pier at a speed of 0.750 m/s. It comes to rest 6.00 m later, damaging the ship, the pier, and the tugboat captain’s finances. Calculate the average force exerted on the pier using the concept of impulse. (Hint: First calculate the time it took to bring the ship to rest.)
$4\text{.}\text{69}\times {\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}\text{N}$ in the boat’s original direction of motion
Calculate the final speed of a 110-kg rugby player who is initially running at 8.00 m/s but collides head-on with a padded goalpost and experiences a backward force of $1\text{.}\text{76}\times {\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{N}$ for $5\text{.}\text{50}\times {\text{10}}^{\text{\u20132}}\phantom{\rule{0.25em}{0ex}}\text{s}$ .
Water from a fire hose is directed horizontally against a wall at a rate of 50.0 kg/s and a speed of 42.0 m/s. Calculate the force exerted on the wall, assuming the water’s horizontal momentum is reduced to zero.
$2\text{.}\text{10}\times {\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\mathrm{N}$ away from the wall
A 0.450-kg hammer is moving horizontally at 7.00 m/s when it strikes a nail and comes to rest after driving the nail 1.00 cm into a board. (a) Calculate the duration of the impact. (b) What was the average force exerted on the nail?
Starting with the definitions of momentum and kinetic energy, derive an equation for the kinetic energy of a particle expressed as a function of its momentum.
When serving a tennis ball, a player hits the ball when its velocity is zero (at the highest point of a vertical toss). The racquet exerts a force of 540 N on the ball for 5.00 ms, giving it a final velocity of 45.0 m/s. Using these data, find the mass of the ball.
60.0 g
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