Problem 1
(a) What is the magnitude of the momentum of a 10,000-kg truck whose speed is 12.0 m/s? (b) What speed would a 2000-kg SUV have to attain in order to have (i) the same momentum? (ii) the same kinetic energy?
Problem 2
In a certain track and field event, the shotput has a mass of 7.30 kg and is released with a speed of 15.0 m/s at 40.0\(^\circ\) above the horizontal over a competitor's straight left leg. What are the initial horizontal and vertical components of the momentum of this shotput?
Problem 4
Two vehicles are approaching an intersection. One is a 2500-kg pickup traveling at 14.0 m/s from east to west (the \(-x\)-direction), and the other is a 1500-kg sedan going from south to north (the \(+y\) direction) at 23.0 m/s. (a) Find the \(x\)- and \(y\)-components of the net momentum of this system. (b) What are the magnitude and direction of the net momentum?
Problem 5
One 110-kg football lineman is running to the right at 2.75 m/s while another 125-kg lineman is running directly toward him at 2.60 m/s. What are (a) the magnitude and direction of the net momentum of these two athletes, and (b) their total kinetic energy?
Problem 6
The mass of a regulation tennis ball is 57 g (although it can vary slightly), and tests have shown that the ball is in contact with the tennis racket for 30 ms. (This number can also vary, depending on the racket and swing.) We shall assume a 30.0-ms contact time. The fastest-known served tennis ball was served by "Big Bill" Tilden in 1931, and its speed was measured to be 73 m/s. (a) What impulse and what force did Big Bill exert on the tennis ball in his record serve? (b) If Big Bill's opponent returned his serve with a speed of 55 m/s, what force and what impulse did he exert on the ball, assuming only horizontal motion?
Problem 7
A 0.0450-kg golf ball initially at rest is given a speed of 25.0 m/s when a club strikes it. If the club and ball are in contact for 2.00 ms, what average force acts on the ball? Is the effect of the ball's weight during the time of contact significant? Why or why not?
Problem 9
A 0.160-kg hockey puck is moving on an icy, frictionless, horizontal surface. At \(t\) = 0, the puck is moving to the right at 3.00 m/s. (a) Calculate the velocity of the puck (magnitude and direction) after a force of 25.0 N directed to the right has been applied for 0.050 s. (b) If, instead, a force of 12.0 N directed to the left is applied from \(t\) = 0 to \(t\) = 0.050 s, what is the final velocity of the puck?
Problem 10
A bat strikes a 0.145-kg baseball. Just before impact, the ball is traveling horizontally to the right at 40.0 m/s; when it leaves the bat, the ball is traveling to the left at an angle of 30\(^\circ\) above horizontal with a speed of 52.0 m/s. If the ball and bat are in contact for 1.75 ms, find the horizontal and vertical components of the average force on the ball.
Problem 11
At time \(t\) = 0 a 2150-kg rocket in outer space fires an engine that exerts an increasing force on it in the \(+x\)-direction. This force obeys the equation \(F_x = At^2\), where \(t\) is time, and has a magnitude of 781.25 N when \(t\) = 1.25 s. (a) Find the SI value of the constant \(A\), including its units. (b) What impulse does the engine exert on the rocket during the 1.50-s interval starting 2.00 s after the engine is fired? (c) By how much does the rocket's velocity change during this interval? Assume constant mass.
Problem 12
Experimental tests have shown that bone will rupture if it is subjected to a force density of 1.03 \(\times\) 10\(^8\) N/m\(^2\). Suppose a 70.0-kg person carelessly rollerskates into an overhead metal beam that hits his forehead and completely stops his forward motion. If the area of contact with the person's forehead is 1.5 cm\(^2\), what is the greatest speed with which he can hit the wall without breaking any bone if his head is in contact with the beam for 10.0 ms?
