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- The x-component of a force on a 46-g golf ball by a 7-iron versus time is plotted in the following figure: Find the x-component of the impulse during the intervals i. [0,50ms] , and ii. [50ms,100ms] Find the change in the x-component of the momentum during the intervals iii. [0,50ms] , and iv. [50ms,100ms]Starting with equations m1v1=m1v1cos1+m2v2cos2 and 0=m1v1cos1+m2v2sin2 for conservation of momentum in the x- and y -directions and assuming that one object is originally stationary, prove that for an elastic collision of two objects of equal masses, 12mv12=12mv22+mv1v2cos(12) as discussed in the text.A cruise ship with a mass of 1.00107 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.)
- Consider the ballistic pendulum device discussed in Example 6.5 and illustrated in Figure 6.13. (a) Determine the ratio of the momentum immediately after the collision to the momentum immediately before the collision, (b) Show that the ratio of the kinetic energy immediately after the collision to the kinetic energy immediately before the collision is m1/(m1 + m2).In Section 1.4, we considered the collision of a karate expert’s hand with a concrete block. Based on the graphs in Figure 1.31, the initial downward speed of the fist with mass 0.75 kg is about -13 m/s and the collision time is approximately 25 ms. Find the impulse and the average force exerted on the block by the fist during the collision.In research in cardiology and exercise physiology, it is often important to know the mast of blood pumped by a persons bran in one stroke. This information can be obtained by means of a ballistocardiograph. The instrument works as follows: The subject lies on a horizontal pallet floating on a film of air. Friction on the pallet is negligible. Initially, the momentum of the system is zero. When the heart beats, it expels a mass m of blood into the aorta with speed v, and the body and platform move in the opposite direction with speed V. The speed of the blood tan be determined independently (e.g., by observing an ultrasound Doppler shift). Assume that the bloods speed is 50.0 cm/s in one typical trial. The mass of the subject plus the pallet is 54.0 kg. The pallet moves at a speed of 6.00 105 m in 0.160 s after one heartbeat. Calculate the mass of blood that leaves the heart. Assume that the mass of blood is negligible compared with the total mass of the person. This simplified example illustrates the principle of ballistocardiography, but in practice a more sophisticated model of heart function is used.
- A basketball with a mass of 0.62 kg falls vertically to the floor where it hits with a speed of 6 m/s. (We take the positive direction to be upward here.) The ball rebounds, leaving the floor with a speed of 4.5 m/s. (a) What impulse acts on the ball during its collision with the floor? (b) If the ball is in contact with the floor for 0.04 s, what is the average force of the ball on the floor?In research in cardiology and exercise physiology, it is often important to know the mass of blood pumped by a persons heart in one stroke. This information can be obtained by means of a ballistocardiograph. The instrument works as follows. The subject lies on a horizontal pallet floating on a film of air. Friction on the pallet is negligible. Initially, the momentum of the system is zero. When the heart beats, it expels a mass m of blood into the aorta with speed , and the body and platform move in the opposite direction with speed V The blood velocity can be determined independently (e.g., by observing the Doppler shift of ultrasound). Assume that it is 50.0 cm/s in one typical trial. The mass of the subject plus the pallet is 54.0 kg. The pallet moves 6.00 10-5 m in 0.160 s after one heartbeat. Calculate the mass of blood that leaves the heart. Assume that the mass of blood is negligible compared with the total mass of the person. (This simplified example illustrates the principle of ballistocardiography, but in practice a more sophisticated model of heart function is used.)Must the total energy of a system be conserved whenever its momentum is conserved? Explain why or why not.
- A 5.50-kg bowling ball moving at 9.00 m/s collides with a 0.850-kg bowling pin, which is scattered at an angle to the initial direction of the bowling ball and with a speed of 15.0 m/s. a. Calculate the final velocity (magnitude and direction) of the bowling ball. b. Is the collision elastic?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).A 1.25-kg wooden block rests on a table over a large hole as in Figure P6.84. A 5.00-g bullet with an initial velocity vi is fired upward into the bottom of the block and remains in the block after the collision. The block and bullet rise to a maximum height of 22.0 cm. (a) Describe how you would find the initial velocity of the bullet using ideas you have learned in this topic, (b) Calculate the initial velocity of the bullet from the information provided.