Exam 9: Linear Momentum and Collisions

A 1.6-kg block is attached to the end of a 2.0-m string to form a pendulum. The pendulum is released from rest when the string is horizontal. At the lowest point of its swing when it is moving horizontally, the block is hit by a 10-g bullet moving horizontally in the opposite direction. The bullet remains in the block and causes the block to come to rest at the low point of its swing. What was the magnitude of the bullet's velocity just before hitting the block?

A 2.0-kg object moving with a velocity of 5.0 m/s in the positive x direction strikes and sticks to a 3.0-kg object moving with a speed of 2.0 m/s in the same direction. How much kinetic energy is lost in this collision?

A rocket engine consumes 450 kg of fuel per minute. If the exhaust speed of the ejected fuel is 5.2 km/s, what is the thrust of the rocket?

At an instant when a particle of mass 50 g has an acceleration of 80 m/s² in the positive x direction, a 75-g particle has an acceleration of 40 m/s² in the positive y direction. What is the magnitude of the acceleration of the center of mass of this two-particle system at this instant?

The linear density of a rod, in g/m, is given by . The rod extends from the origin to x = 0.400 m. What is the mass of the rod?

A 2.0-kg object moving 5.0 m/s collides with and sticks to an 8.0-kg object initially at rest. Determine the kinetic energy lost by the system as a result of this collision.

A 10-g bullet moving 1000 m/s strikes and passes through a 2.0-kg block initially at rest, as shown. The bullet emerges from the block with a speed of 400 m/s. To what maximum height will the block rise above its initial position? ​ ​

A 1.5-kg playground ball is moving with a velocity of 3.0 m/s directed 30° below the horizontal just before it strikes a horizontal surface. The ball leaves this surface 0.50 s later with a velocity of 2.0 m/s directed 60° above the horizontal. What is the magnitude of the average resultant force on the ball?

A U-238 nucleus (mass = 238 units) decays, transforming into an alpha particle (mass = 4.00 units) and a residual thorium nucleus (mass = 234 units). If the uranium nucleus was at rest, and the alpha particle has a speed of 1.50 × 10⁷ m/s, determine the recoil speed of the thorium nucleus.

A uniform thin wire has a length and is bent into a semicircular arc of radius R. If the wire starts at (x, y) = (R, 0) and curves counterclockwise to (x, y) = (−R, 0), what is the y coordinate of its center of mass?

Two cars start at the same point, but travel in opposite directions on a circular path of radius R, each at speed v. While each car travels a distance less than , one quarter circle, the center of mass of the two cars

A 3.0-kg mass is released from rest at point A of a circular frictionless track of radius 0.40 m as shown in the figure. The mass slides down the track and collides with a 1.4-kg mass that is initially at rest on a horizontal frictionless surface. If the masses stick together, what is their speed after the collision?

Refer to Exhibit 9-1. What is the horizontal component of their momentum, in , immediately after the collision?

The value of the momentum of a system is the same at a later time as at an earlier time if there are no

A 1.0-kg ball is attached to the end of a 2.5-m string to form a pendulum. This pendulum is released from rest with the string horizontal. At the lowest point in its swing when it is moving horizontally, the ball collides elastically with a 2.0-kg block initially at rest on a horizontal frictionless surface. What is the speed of the block just after the collision?

Refer to Exhibit 9-1. What is the magnitude of their velocity, in m/s, immediately after the collision?

Three particles are placed in the xy plane. A 30-g particle is located at (3, 4) m, and a 40-g particle is located at (−2, −2) m. Where must a 20-g particle be placed so that the center of mass of the three-particle system is at the origin?

A steel ball bearing of mass m₁ and speed of magnitude v₁ has a head-on elastic collision with a steel ball bearing of mass m₂ at rest. Rank the speed v₁ of m₁ relative to v₂, the magnitude of the speed of m₂, after the collision when i) m₁ > m₂; ii) m₁ = m₂; and iii) m₁ < m₂.

A 10-g bullet moving horizontally with a speed of 2.0 km/s strikes and passes through a 4.0-kg block moving with a speed of 4.2 m/s in the opposite direction on a horizontal frictionless surface. If the block is brought to rest by the collision, what is the kinetic energy of the bullet as it emerges from the block?

An 80-g particle moving with an initial speed of 50 m/s in the positive x direction strikes and sticks to a 60-g particle moving 50 m/s in the positive y direction. How much kinetic energy is lost in this collision?