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Professional Application
Explain in terms of impulse how padding reduces forces in a collision. State this in terms of a real example, such as the advantages of a carpeted vs. tile floor for a day care center.
While jumping on a trampoline, sometimes you land on your back and other times on your feet. In which case can you reach a greater height and why?
Professional Application
Tennis racquets have “sweet spots.” If the ball hits a sweet spot then the player's arm is not jarred as much as it would be otherwise. Explain why this is the case.
A bullet is accelerated down the barrel of a gun by hot gases produced in the combustion of gun powder. What is the average force exerted on a 0.0300-kg bullet to accelerate it to a speed of 600 m/s in a time of 2.00 ms (milliseconds)?
$9\text{.}\text{00}\times {\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\mathrm{N}$
Professional Application
A car moving at 10 m/s crashes into a tree and stops in 0.26 s. Calculate the force the seat belt exerts on a passenger in the car to bring him to a halt. The mass of the passenger is 70 kg.
A person slaps her leg with her hand, bringing her hand to rest in 2.50 milliseconds from an initial speed of 4.00 m/s. (a) What is the average force exerted on the leg, taking the effective mass of the hand and forearm to be 1.50 kg? (b) Would the force be any different if the woman clapped her hands together at the same speed and brought them to rest in the same time? Explain why or why not.
a) $2\text{.}\text{40}\times {\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{N}$ toward the leg
b) The force on each hand would have the same magnitude as that found in part (a) (but in opposite directions by Newton’s third law) because the change in momentum and the time interval are the same.
Professional Application
A professional boxer hits his opponent with a 1000-N horizontal blow that lasts for 0.150 s. (a) Calculate the impulse imparted by this blow. (b) What is the opponent’s final velocity, if his mass is 105 kg and he is motionless in midair when struck near his center of mass? (c) Calculate the recoil velocity of the opponent’s 10.0-kg head if hit in this manner, assuming the head does not initially transfer significant momentum to the boxer’s body. (d) Discuss the implications of your answers for parts (b) and (c).
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 magnitude of 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.
$\begin{array}{}\mathbf{p}=m\mathbf{v}\Rightarrow {p}^{2}={m}^{2}{v}^{2}\Rightarrow \frac{{p}^{2}}{m}={\mathrm{mv}}^{2}\\ \Rightarrow \frac{{p}^{2}}{2m}=\frac{1}{2}{\mathrm{mv}}^{2}=\text{KE}\\ \text{KE}=\frac{{p}^{2}}{2m}\end{array}$
A ball with an initial velocity of 10 m/s moves at an angle $\text{60\xba}$ above the $+x$ -direction. The ball hits a vertical wall and bounces off so that it is moving $\text{60\xba}$ above the $-x$ -direction with the same speed. What is the impulse delivered by the wall?
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
A punter drops a ball from rest vertically 1 meter down onto his foot. The ball leaves the foot with a speed of 18 m/s at an angle $\text{55\xba}$ above the horizontal. What is the impulse delivered by the foot (magnitude and direction)?
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