Exam 5: Centre of Mass and Linear Momentum

A pair of railway boxcars are moving toward each other on a rail with negligible friction. One boxcar is twice the mass of the other. On collision, the boxcars couple to each other. In order for the coupled pair to have zero velocity (relative to a bystander next to the track) after the collision, what is the ratio of velocities of the more massive to the less massive boxcar before the collision?

In order for a rigid body suspended by a pivot to be in rotational equilibrium, its point of suspension must be vertically above its centre of gravity.

A spaceship and docking module travelling in parallel come alongside each other at the same speed. The module fires a small rocket at a right angle to its motion to bring the module into contact with the spaceship for docking. On docking, which one of these effects does this have on the motion of the combined craft?

A standard man (m = 70 kg) is holding a 300 g marble in his hand. The values for the masses of the hand, forearm, and upper arm, expressed as the percentage of full body mass, are as follow: hand 0.65%, forearm 1.87%, and upper arm 3.25%. Each segment's weight acts as if the mass is concentrated in the centre of mass of a segment. The points at which the weight of each segment is acting are shown in Fig. 5.1. Calculate the centre of mass of the arm.

An astronaut in a space capsule is experiencing "weightlessness"; therefore, he does not have to exert any force in order to throw a ball, which is also weightless.

When firing a rifle, you experience a force against your shoulder. Explain why.

A ball rolls in a straight line without friction across the horizontal floor of a descending elevator. As the elevator comes to a stop, which of the following happens to the ball?

One to simulate gravity in a spaceship is to set the spaceship into rotation at constant angular velocity. Describe what shape the spaceship would have in order for this to work.

A fireman is sliding down a fire pole. As he speeds up, he tightens his grip on the pole, thus increasing the vertical frictional force that the pole exerts on the fireman. When this force equals the weight of the fireman, which of the following happens?

Assuming a classical picture of the atom, an electron is captured into a circular orbit about a spherically shaped, singly charged ion, thus neutralizing it. In the frame of reference of the ion, the neutral atom acquires a component of velocity that is

Impulse is a vector.

The mass of a human leg below the knee is 0.60 of the mass above the knee, and its centre of mass is located at 0.3 of the length of the lower leg from the knee joint. When the leg is bent from straight to a right angle at the knee, by what amount does the centre of mass of the leg shift? Express your answer in terms of the length of the leg below the knee.

The thigh has a mass of 21.5 units, and its centre of mass is 9.6 units from the hip joint. The corresponding mass and length units for the knee are 9.6, 33.9; and for the ankle, 3.4, 50.3. Where is the centre of mass of the outstretched leg located relative to the hip bone?

A net force of 100.0 N is applied to a certain object. As a result, the object accelerates with an acceleration of G)What is the mass of the object?

Two cars of equal mass, one travelling north and the other east, collide at the same speed at right angles to each other. Assuming the collision is inelastic, what is the velocity following the collision?

When you catch a ball, you feel a force against your hand. Explain why.

If the gravitational forces of bodies outside the solar system were neglected, the Sun would move at a constant velocity.

You are falling from your tree house. Which of these actions could slow the fall? Ignore the effects of air resistance.

A railway boxcar is moving toward a stationary boxcar on a rail with negligible friction. The stationary boxcar is twice the mass of the moving one. On collision, the boxcars couple to each other. After the collision, what is the velocity of the more massive boxcar? Express your answer as a fraction of the velocity of the less massive boxcar before the collision.

A source of alpha particles bombards a target of gold. A small fraction of alpha particles return in a direction opposite to that of the ingoing source particles. Which of the following statements accurately describes the cause of this phenomenon?