Exam 9: Linear Momentum

A long thin rod of length L has a linear density λ(x) = A(L-x⁾² where x is the distance from the left end of the rod. (a) How far is the center of mass of the rod from the left end of the rod? (b) What is the mass of the rod?

The linear momentum of an extended object is the product of the object's mass and the velocity of its center of mass.

The impulse delivered to an object is equal to the change in the object's velocity.

A 2.00-m rod of negligible mass connects two small objects. The mass of one object is 1.00 kg and the mass of the other is unknown. The center of mass of this system is on the rod a distance 1.80 m from the 1.00-kg mass object. What is the mass of the other object?

A 1000-kg car is traveling north at 20.0 m/s. A 1500-kg car is traveling north at 36.0 m/s. The 1500-kg collides with the rear of the 1000-kg car and they lock together. Ignoring external forces acting during the collision, what is the velocity of the cars immediately after the collision?

A plane, flying horizontally, releases a bomb, which explodes before hitting the ground. Neglecting air resistance, the center of mass of the bomb fragments, just after the explosion

A rocket with a mass of 2.0 × 10⁶ kg is designed to take off from the surface of the earth by burning fuel and ejecting it with an exhaust speed of 3500 m/s. What is the minimum rate at which the fuel should be consumed in order to attain liftoff?

At what speed must a 150-kg football player be moving to have the same momentum as a 15.0-g bullet traveling at 300 m/s?

A 2.00-kg mass object traveling east at 20.0 m/s collides with a 3.00-kg mass object traveling west at 10.0 m/s. After the collision, the 2.00-kg mass has a velocity 5.00 m/s to the west. How much kinetic energy was lost during the collision?

Two automobiles traveling at right angles to each other collide and stick together. Car A has a mass of 1200 kg and had a speed of 25 m/s before the collision. Car B has a mass of 1600 kg. The skid marks show that, immediately after the collision, the wreckage was moving in a direction making an angle of 40° with the original direction of car A. What was the speed of car B before the collision?

An interacting system of two objects has no external force acting on the system. The first object has a mass 2.00 kg and is moving with a velocity (2.00 m/s) + (1.00 m/s) at time t = 0.00 s. The second object has a mass 3.00 kg and is moving with a velocity (-1.00 m/s) + (1.00 m/s) at time t = 0.00 s. The second object is moving with a velocity (2.00 m/s) + (-1.00 m/s) at time t = 1.00 s. (a) What is the total momentum of the system at time t = 0.00 s? (b) What is the velocity of the first object at t = 1.00 s?

A novice marksman fires a rifle while holding the butt of the rifle a couple of centimeters away from his shoulder. Explain what happens in terms of the physical principles involved.

Explain the significance of the center of gravity.

An elastic collision of two objects is characterized by the following.

Define an elastic collision in terms of conservation of momentum and energy.

A Ping-Pong ball moving east at a speed of 4 m/s, collides with a stationary bowling ball. The Ping-Pong ball bounces back to the west, and the bowling ball moves very slowly to the east. Which object experiences the greater magnitude impulse during the collision?

A 320-g air track cart is traveling at 1.25 m/s and a 270-g cart traveling in the opposite direction at 1.33 m/s. What is the speed of the center of mass of the two carts?

An inelastic collision of two objects is characterized by the following.

If two objects stick together as a result of a collision, the collision is said to be perfectly elastic.

The change in the momentum vector is in the direction of the net force.