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Exam 5: Centre of Mass and Linear Momentum

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Question 1

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Three railway cars of equal mass are on the same (frictionless) track. The one on the left is moving with velocity V toward the other two which are stationary. As the cars undergo successive collisions, they couple and move together. What is the velocity of the final configuration of the three coupled cars?

A) V
B) V/2
C) V/3
D) V/4

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Question 2

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A ball rolling across the centre line of a long level table collides with a second ball of equal mass also on the centre line. Both balls fall off the edge of the table at the same instant of time.

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Question 3

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Discuss the advantages to passenger safety if a car undergoes an inelastic collision with another car compared to an elastic collision.

Describe the mechanical principle of why air bags are used in cars.

A fish swimming with speed of 1.00 m/s is chasing its prey of 0.100 of its mass. It captures its prey when their relative velocity is 0.10 m/s. If the fish were to capture its prey when their relative velocity was 0.20 m/s, what would be the velocity of the fish in the second case relative to the first case?

Explain whether someone inside a closed box on the ground would be able to tell the difference from being in a spaceship accelerating at g perpendicular to the ground.

Two balls of equal mass are thrown toward each other with the same speed and at the same angle to the horizontal by two people standing a certain distance apart on the ground. Following an elastic collision, the balls will always return to their respective throwers with the same speed.

Find the centre of mass of a water molecule. Angles and distances are shown in Fig. 5.2. The mass of a hydrogen atom is 1.0 u, and the mass of an oxygen atom is 16 u, where u is the atomic mass unit. Choose an appropriate coordinate system.

An object is moving with constant velocity. Which of these statements accurately describes this?

A person inside an elevator throws a ball horizontally through the air. Describe under what conditions the ball would travel in a straight line.

A squid ejects a bolus of water in order to escape a predator. The squid has a mass of 0.4 kg with its water cavity empty, and needs to escape with a speed of at least 0.8 m/s. If the ejected water has a mass of 0.1 kg, how fast must it be ejected in order for the squid to escape?

Explain why Newton's second law is expressed in terms of momentum rather than "mass times acceleration." Give an example of where this difference matters.

A snowball moving with a certain velocity in interstellar space evaporates molecules from its surface at an equal rate in all directions. The velocity of the snowball remains constant throughout the evaporation.

The metal head of a hammer is loose. In order to get the hammerhead tight again, you should drop the hammer with the head end down.

A car of mass m travelling at 40.0 km/hr collides head-on with a stationary car of equal mass, and stays attached until the pair come to a stop. The car in motion does NOT apply the brakes, whereas the stationary car has a braking force of 0.2mg. At what distance from the collision site does the pair of cars come to rest?

There are 15 billiard balls in a rack. The rack is removed. The balls are in triangular formation with the tip toward the cue ball. The cue ball is shot into the ball on the tip of the triangle. Assuming all balls have the same mass, in which direction does the net velocity vector of the set of balls point soon after the cue ball strikes them?

An astronaut in a space capsule is experiencing "weightlessness." Does the astronaut have to exert any effort to throw a bowling ball, since the bowling ball is also weightless?

A 1000 kg car moving at 20 km/hr collides inelastically and head-on with a 10000 kg truck moving at 2 km/hr. Which one of these statements correctly describes the motion of the two vehicles after the collision?

Interplanetary spaceships can be sent to distant parts of the solar system by means of the "gravitational slingshot" method. The spaceship makes a brief close encounter with a massive planet and is flung away in a different direction of travel. Assuming the approach and post-encounter directions of the spaceship, as seen from the planet, are opposite to each other, describe how the spaceship may increase its overall velocity relative to the Sun.

For a single rigid body, its centre of mass always lies inside the body.