Exam 9: Linear Momentum and Collisions

A 3.0-kg mass sliding on a frictionless surface explodes into three 1.0-kg masses. After the explosion the velocities of the three masses are: (1) 9.0 m/s, north; (2) 4.0 m/s, 30° south of west; and (3) 4.0 m/s, 30° south of east. What was the magnitude of the original velocity of the 3.0-kg mass?

A 5.0-g particle moving 60 m/s collides with a 2.0-g particle initially at rest. After the collision each of the particles has a velocity that is directed 30° from the original direction of motion of the 5.0-g particle. What is the speed of the 2.0-g particle after the collision?

The speed of a 2.0-kg object changes from 30 m/s to 40 m/s during a 5.0-s time interval. During this same time interval, the velocity of the object changes its direction by 90°. What is the magnitude of the average total force acting on the object during this time interval?

An astronaut outside a spaceship hammers a loose rivet back in place. What happens to the astronaut as he swings the hammer?

A ball falls to the ground from height h and bounces to height h'. Momentum is conserved in the ball-earth system

A 1.6-kg ball is attached to the end of a 0.40-m string to form a pendulum. This pendulum is released from rest with the string horizontal. At the lowest point of its swing, when it is moving horizontally, the ball collides with a 0.80-kg block initially at rest on a horizontal frictionless surface. The speed of the block just after the collision is 3.0 m/s. What is the speed of the ball just after the collision?

A 1.0-kg object moving 9.0 m/s collides with a 2.0-kg object moving 6.0 m/s in a direction that is perpendicular to the initial direction of motion of the 1.0-kg object. The two masses remain together after the collision, and this composite object then collides with and sticks to a 3.0-kg object. After these collisions, the final composite (6.0-kg) object remains at rest. What was the speed of the 3.0-kg object before the collisions?

A 500-g firework explodes into two pieces of equal mass at an instant when it is traveling straight up at 10 m/s. If one half shoots off horizontally to the left at 20 m/s, what is the velocity, in m/s, of the other half immediately after the explosion? (The x axis is directed right; the y axis up.)

A 4.0-kg particle is moving horizontally with a speed of 5.0 m/s when it strikes a vertical wall. The particle rebounds with a speed of 3.0 m/s. What is the magnitude of the impulse delivered to the particle?

Stan argues that momentum cannot be conserved when a collision is not a head-on collision. Rachel insists it is conserved because each body receives an impulse of equal magnitude. Rachel is correct because

A 1.2-kg object moving with a speed of 8.0 m/s collides perpendicularly with a wall and emerges with a speed of 6.0 m/s in the opposite direction. If the object is in contact with the wall for 2.0 ms, what is the magnitude of the average force on the object by the wall?

High-speed stroboscopic photographs show that the head of a golf club of mass 200 grams is traveling at 55.0 m/s just before it strikes a 46.0-gram golf ball at rest on a tee. After the collision, the clubhead travels (in the same direction) at 40.0 m/s. Find the speed of the golf ball just after impact.

In an elastic collision between two bodies of equal mass, with body 2 initially at rest, body 1 moves off at angle θ relative to the direction of its initial velocity and body 2 at angle φ. The sine of the sum of θ and φ, sin(θ + φ), is equal to

A 4.0-kg mass has a velocity of 4.0 m/s, east when it explodes into two 2.0-kg masses. After the explosion one of the masses has a velocity of 3.0 m/s at an angle of 60° north of east. What is the magnitude of the velocity of the other mass after the explosion?

A rocket with an initial mass of 1000 kg adjusts its thrust by varying the rate at which mass is ejected. The ejection speed relative to the rocket is 40 km/s. If the acceleration of the rocket is to have a magnitude of 20 m/s² at an instant when its mass is 80% of the original mass, at what rate is mass being ejected at that instant? Ignore any external forces on the rocket.

A 2.4-kg ball falling vertically hits the floor with a speed of 2.5 m/s and rebounds with a speed of 1.5 m/s. What is the magnitude of the impulse exerted on the ball by the floor?

An exam paper contains the following equation for rocket propulsion: . The error in the equation is that, instead of (v + v_e), the velocity of the fuel relative to the ground should be

A 5.0-kg mass with an initial velocity of 4.0 m/s, east collides with a 4.0-kg mass with an initial velocity of 3.0 m/s, west. After the collision the 5.0-kg mass has a velocity of 1.2 m/s, south. What is the magnitude of the velocity of the 4.0-kg mass after the collision?

Two blocks with masses 2.0 kg and 3.0 kg are placed on a horizontal frictionless surface. A light spring is placed in a horizontal position between the blocks. The blocks are pushed together, compressing the spring, and then released from rest. After contact with the spring ends, the 3.0-kg mass has a speed of 2.0 m/s. How much potential energy was stored in the spring when the blocks were released?

A ball of mass m_B is released from rest and acquires velocity of magnitude v_B before hitting the ground. The ratio of the kinetic energy the Earth acquires to the kinetic energy the ball acquires is