50. | Sports doctors are very concerned about brain injuries in con- BIO tact sports. Brain injuries can occur if the head accelerates or decelerates at more than 50g, with injuries becoming serious or even life-threatening at 150g. Padded helmets are designed to re- duce forces by lengthening the contact time. Suppose two 95 kg football players each running at 4.5 m/s have a (illegal) head-to- head collision that brings both of them to a halt. A real collision of this sort is complex, but we can model it as a simple collision in which the force is constant for the duration of the collision. a. What magnitude force would decelerate each player at 75g? b. What is the minimum collision duration in ms for which their head accelerations would not exceed 75g? c. For players who are not wearing helmets, a true head-to- head collision has a duration of approximately 2.0 ms. In such a situation, what would be the head deceleration in g's of these two players?

50. | Sports doctors are very concerned about brain injuries in con- BIO tact sports. Brain injuries can occur if the head accelerates or decelerates at more than 50g, with injuries becoming serious or even life-threatening at 150g. Padded helmets are designed to re- duce forces by lengthening the contact time. Suppose two 95 kg football players each running at 4.5 m/s have a (illegal) head-to- head collision that brings both of them to a halt. A real collision of this sort is complex, but we can model it as a simple collision in which the force is constant for the duration of the collision. a. What magnitude force would decelerate each player at 75g? b. What is the minimum collision duration in ms for which their head accelerations would not exceed 75g? c. For players who are not wearing helmets, a true head-to- head collision has a duration of approximately 2.0 ms. In such a situation, what would be the head deceleration in g's of these two players?

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Description: 50. | Sports doctors are very concerned about brain injuries in con-BIO tact sports. Brain injuries can occur if the head accelerates ordecelerates at more than 50g, with injuries becoming serious oreven life-threatening at 150g. Padded helmets are

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter5: The Laws Of Motion

Section: Chapter Questions

Problem 5.20CQ: Balancing carefully, three boys inch out onto a horizontal tree branch above a pond, each planning...

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The front 1.20 m of a 1 400-kg car is designed as a crumple zone that collapses to absorb the shock of a collision. If a car traveling 25.0 m/s stops uniformly in 1.20 m, (a) how long does the collision last, (b) what is the magnitude of the average force on the car, and (c) what is the acceleration of the car? Express the acceleration as a multiple of the acceleration of gravity.
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. Assume constant acceleration of the hammer-nail pair. a. Calculate the duration of the impact. b. What was the average force exerted on the nail?
A 50.0 kg driver is riding at 35.0 m/s in her red sports car when she must suddenly slam on the brakes to avoidhitting a deer crossing the road. She strikes the air bag, which brings her body to a stop in 0.500 s.a. What average force does the seat belt exert on her? b. If she had not been wearing her seat belt and not had an air bag, then the windshield would have stopped herhead in 0.002 s. What average force would the windshield have exerted on her? c. What is the impulse delivered to her when the air bag changes her momentum? d. What is the impulse delivered to her when the windshield changes her momentum? e. Compare the two impulses calculated in c and d and justify the results.
A 200 kgkg weather rocket is loaded with 100 kgkg of fuel and fired straight up. It accelerates upward at 35 m/s2m/s2 for 32 ss, then runs out of fuel. Ignore any air resistance effects. What is the rocket's maximum altitude?
In baseball, a pitcher can accelerate a 0.15-kg ball from rest to 98 mi>h in a distance of 1.7 m. (a) What isthe average force exerted on the ball during the pitch? (b) If themass of the ball is increased, is the force required of the pitcherincreased, decreased, or unchanged? Explain.
(1) A car with mass 996 kg moving at 28 m/s hits a giant bag of marshmallows. The bag slows the car down, but it is unable to completely stop it because it ruptures at Dt = 1.8 s after the car hits, scattering marshmallows all over the countryside. Suppose the bag exerts a force on the car that depends on time (t) given by F = -At2; A = 7.2 x 103 N/s2 when t is in seconds (2) Two objects, moving towards each other with speed v, collide head on, stick together, and then move on with speed v/4 after the collision. (a) What is the ratio of the kinetic energy after the collision to the kinetic energy before the collision? (answer: 1/16) (b) What is the ratio of the mass of the more massive object to the mass of the less massive object? (answer: 5/3)
Balancing carefully, three boys inch out onto a horizontal tree branch above a pond, each planning to dive in separately. The third boy in line notices that the branch is barely strong enough to support them. He decides to jump straight up and land back on the branch to break it, spilling all three into the pond. When he starts to carry out his plan, at what precise moment does the branch break? Explain. Suggestion: Pretend to be the third boy and imitate what he does in slow motion. If you are still unsure, stand on a bathroom scale and repeat the suggestion.
A man claims he ran safely hold on to a 12.0-kg child in a head-on collision with a relative speed of 120-mi/h lasting for 0.10 s as long as he has his seat belt on. (a) Find the magnitude of the average force needed to hold onto the child, (b) Based on the result to part (a), is the mans claim valid? (c) What does the answer to this problem say about laws requiring the use of proper safely devices such as seat belts and special toddler seats?
A 75.0-kg ice skater moving at 10.0 m/s crashes into a stationary skater of equal mass. After the collision, the two skaters move as a unit at 5.00 m/s. Suppose the average force a skater can experience without breaking a bone is 4 500 N. If the impact time is 0.100 s, does a bone break?
(a) If two automobiles collide, they usually do not stick together. Does this mean the collision is elastic? (b) Explain why a head-on collision is likely to be more dangerous than other types of collisions.
The average speed of a nitrogen molecule in air is about 6.70 102 m/s, and its mass is 4.68 1026 kg. (a) If it takes 3.00 1015 s for a nitrogen molecule to hit a wall and rebound with the same speed but moving in the opposite direction, what is the average acceleration of the molecule during this time interval? (b) What average force does the molecule exert on the wall?
(a) If the rocket sled shown in Figure 4.32 starts with only one rocket burning, what is the magnitude of its acceleration? Assume that the mass of the system is 2100 kg, the thrust T is 2.4104 N, and the force of friction opposing the motion is known to be 650 N. (b) Why is the acceleration not one-fourth of what it is with all rockets burning?