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Exam 7: Momentum, Impulse, and Collisions

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Question 1

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The dimensional equivalence of the quantity "momentum" in terms of the fundamental quantities (mass, length, time) is:

A) MLT^-1.
B) ML²T^-2.
C) MLT.
D) MLT^-2.

E) None of the above
F) A) and B)

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Question 2

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A billiard ball is moving in the x direction at 30.0 cm/s and strikes another billiard ball moving in the y direction at 40.0 cm/s. As a result of the collision, the second ball moves at 50.0 cm/s, and the first ball stops. In what final direction does the second ball move?

A) in the x direction
B) at an angle of 45.0^o ccw from the x direction
C) at an angle of 53.1^o ccw from the x direction
D) Such a collision cannot happen.

E) B) and C)
F) B) and D)

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Question 3

Multiple Choice

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Three masses are positioned along the x-axis. Their masses and positions are: with , with , and with . What is the x-coordinate of center of mass of this system?

A model car is propelled by a cylinder of carbon dioxide gas. The cylinder emits gas at a rate of 4.5 g/s with an exit speed of 80.0 m/s. The car has a mass of 200 g, including the CO₂ cylinder. Starting from rest, what is the car's initial acceleration?

The kinetic energy of an object is quadrupled. Its momentum will change by what factor?

A 4.0 ft by 8.0 ft sheet of plywood of uniform density and thickness lies in the 1^st quadrant with its long side along the x axis, one corner at the origin, and the diagonally opposite corner at position (x, y) = (8.0 ft, 4.0 ft) . The lower right 2.0 ft by 4.0 ft quarter of the sheet is removed from the sheet. What are the coordinates of the center of mass of the remaining portion of the sheet?

A 2500-kg truck moving at 10.00 m/s strikes a car waiting at a traffic light, hooking bumpers. The two continue to move together at 6.00 m/s. What was the mass of the struck car?

In a system with two moving objects, when a collision occurs between the objects:

A rock is moving with speed v. If the mass of the rock were tripled and the speed were reduced to v/3, which of the following statements would be true?

A helicopter stays aloft by pushing large quantities of air downward every second. What mass of air must be pushed downward at 30.0 m/s every second to keep a 1000 kg helicopter aloft?

Kaitlin uses a bat to hit a thrown baseball. She knocks the ball back in the direction from which it came in an inelastic collision. The bat, which is heavier than the baseball, continues to move in the same direction after the hit as Kaitlin "follows through." Is the ball moving faster before or after it was hit?

Alex throws a 0.15-kg rubber ball down onto the floor. The ball's speed just before impact is 6.5 m/s and just after is 3.5 m/s. If the ball is in contact with the floor for 0.050 s, what is the magnitude of the average force applied by the floor on the ball?

A neutron in a nuclear reactor makes an elastic head-on collision with a carbon atom initially at rest. (The mass of the carbon atom is 12 times that of the neutron.) What fraction of the neutron's original kinetic energy is retained by the neutron?

A machine gun is attached to a railroad flatcar that rolls with negligible friction. If the railroad car has a mass of 6.25 * 10⁴ kg, how many bullets of mass 25 g would have to be fired at 250 m/s off the back to give the railroad car a forward velocity of 0.3 m/s?

A uranium nucleus (mass 238 units) at rest decays into a helium nucleus (mass 4.0 units) and a thorium nucleus (mass 234 units) . If the speed of the helium nucleus is 1.8 * 10⁶ m/s, what is the speed of the thorium nucleus?

At liftoff, the engines of the Saturn V rocket consumed 14,000 kg/s of fuel and exhausted the combustion products at 2900 m/s. What was the total upward force (thrust) provided by the engines?

Two skaters, both of mass 75 kg, are initially at rest on skates on a frictionless ice pond. One skater throws a 0.3-kg ball at 10 m/s to his friend, who catches it and throws it back at 10 m/s. When the first skater has caught the returned ball, what is the velocity of each of the two skaters?

In an automobile collision, how does an airbag lessen the blow to the passenger? Assume as a result of the collision, the passenger stops.

The law of conservation of momentum is applicable to systems made up of objects described by which of the following?

A billiard ball (Ball #1) moving at 5.00 m/s strikes a stationary ball (Ball #2) of the same mass. After the elastic collision, Ball #1 moves at a speed of 3.50 m/s. Find the speed of Ball #2 after the collision.