PHYS 2211 Module 9 Self Assessment Practice Problems

Module 9 Self Assessment Practice Problems

9.1

A 75.0-kg person is riding in a car moving at 20.0 m/s when the car runs into a bridge abutment (see the figure).
(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.
Answer: (a) 1.5 x 106 N (b) 1.0 x 105 N
9.2
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?
Answer: (a) 2.86 x 10-3 s (b) 1.1 x 103 N
9.3

A hockey puck of mass 150 g is sliding due east on a frictionless table with a speed of 10 m/s. Suddenly, a constant force of magnitude 5 N and direction due north is applied to the puck for 1.5 s. Find the north and east components of the momentum at the end of the 1.5-s interval.
Answer: 7.5 kg•m/s North and 1.5 kg•m/s East
9.4

The figure shows a bullet of mass 200 g traveling horizontally towards the east with speed 400 m/s, which strikes a block of mass 1.5 kg that is initially at rest on a frictionless table. After striking the block, the bullet is embedded in the block and the block and the bullet move together as one unit.
(a) What is the magnitude and direction of the velocity of the block/bullet combination immediately after the impact?
(b) What is the magnitude and direction of the impulse by the block on the bullet?
(c) What is the magnitude and direction of the impulse from the bullet on the block?
(d) If it took 3 ms for the bullet to change the speed from 400 m/s to the final speed after impact, what is the average force between the block and the bullet during this time?
Answer: (a) 47 m/s in the bullet to block direction (b) 70.6 N•s toward the bullet (c) 70.6 N•s toward the block (d) 2.35 x 104 N
9.5
Two figure skaters are coasting in the same direction, with the leading skater moving at 5.5 m/s and the trailing skating moving at 6.2 m/s. When the trailing skater catches up with the leading skater, he picks her up without applying any horizontal forces on his skates. If the trailing skater is 50% heavier than the 50-kg leading skater, what is their speed after he picks her up?
Answer: 5.9 m/s
9.6
A 2000-kg railway freight car coasts at 4.4 m/s underneath a grain terminal, which dumps grain directly down into the freight car. If the speed of the loaded freight car must not go below 3.0 m/s, what is the maximum mass of grain that it can accept?
Answer: 9.3 x 102 kg
9.7
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 of 15.8° 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? How do you know?
Answer: (a) 6.80 m/s, 5.33° (b) yes
9.8
An oxygen atom (mass 16 u) moving at 733 m/s at 15° with respect to the direction collides and sticks to an oxygen molecule (mass 32 u) moving at 528 m/s at 128° with respect to the direction. The two stick together to form ozone. What is the final velocity of the ozone molecule?
Answer: 341 m/s at 86.8° with respect to the axis.
9.9

Three point masses are placed at the corners of a triangle as shown in the figure. Find the center of mass of the three-mass system.
Answer: With the origin defined to be at the position of the 150-g mass, xcm = -1.23 cm and ycm = 0.69 cm
9.10
If 1% of the Earth’s mass were transferred to the Moon, how far would the center of mass of the Earth-Moon system move? The mass of the Earth is 5.97 x 1024 kg and that of the Moon is 7.34 x 1022 kg. The radius of the Moon’s orbit is about 3.84 x 105 m.
Answer: 3787 m