Exam 8: Systems of Particles and Conservation of Linear Momentum

An object of mass M₁ is moving with a speed v on a straight, level, frictionless track when it collides with another mass M₂ that is at rest on the track. After the collision, M₁ and M₂ stick together and move with a speed of

A 7000-kg coal car of a train coasts at 7.0 m/s on a frictionless track when a 3000-kg load of coal is dropped vertically onto the car. The coal car's speed after the coal is added is

Using a mallet, you strike a ball of mass 0.50 kg that is initially at rest. The force F on the ball as a function of time is plotted in the figure. At t = 2.0 ms, the speed of the ball is

A Saturn V rocket with an initial mass m₀ of 3 $\times$ 10⁶ kg has a payload that accounts for 27% of this mass, a burn rate of 15 $\times$ 10³ kg/s, and a thrust F_th of 35 $\times$ 10⁶ N. The exhaust speed is

A block of mass 5 kg slides down a frictionless track from a height of 1.5 m. It collides with a second mass of 8 kg. The two blocks stick together and after the impact they begin to slide on a rough surface with a coefficient of kinetic friction of 0.65 until coming to rest. Calculate how far, d, the blocks slide on the rough surface.

A moving particle is stopped by a single head-on collision with a second, stationary particle if the moving particle undergoes

A projectile with a mass 6M is fired at a speed of 400 m/s at an angle of 60º above the horizontal. At the highest point of its trajectory, the projectile is broken into two equal pieces by an internal explosion. Just after the explosion, one of the two pieces is known to be traveling vertically downward at a speed of 300 m/s. The magnitude of the velocity of the other half of the projectile is

A 200-g ball dropped from a height of 50 cm rebounds to a height of 35 cm after impact. The change in momentum of the ball is

The center of mass of a system of particles is so defined that

A ball of mass m strikes a wall that is perpendicular to its path at speed +v and rebounds in the opposite direction with a speed -v. The impulse imparted to the ball by the wall is

What is the physical significance of the area under the curve shown in the figure?

Water is fired horizontally out of a 7-cm diameter hose directly onto a wall at a speed of 7m/s. Assuming that the water after impact falls straight down the wall, the average force on the wall is (density of water = 1000 kg/m³ )

An 1810-kg truck traveling eastward at 64.4 km/h collides at an intersection with a 905-kg automobile traveling northward at 96.5 km/h. The vehicles lock together and immediately after the collision are headed in which direction?

Two identical masses are hung on strings of the same length. One mass is released from a height h above its free-hanging position and strikes the second mass; the two stick together and move off. They rise to a height H given by

A bullet (mass = m₁) is fired at speed V into a block of mass m₂ at rest. If the bullet escapes from the block with only a third of its original speed then the recoil speed of the block is given by

Five billiard balls are in contact and at rest on a wire that passes through their centers. Two billiard balls are slammed into one end of the row of five at a velocity . If the balls are free to slide but not roll and if the collision is elastic, which of the following is most likely to take place?

An automobile of mass 1300 kg has an initial velocity of 7.20 m/s toward the north and a final velocity of 6.50 m/s toward the west. The magnitude and direction of the change in momentum of the car are

A Saturn V rocket with an initial mass m₀ of 3 $\times$ 10⁶ kg has a payload that accounts for 27% of this mass, a burn rate of 15 $\times$ 10³ kg/s, and a thrust F_th of 35 $\times$ 10⁶ N. The acceleration at lift-off is

If you take the derivative of the kinetic energy of a particle with respect to its velocity, you get

A body is acted on by an impulsive force from time t = 0 to time t = 10 ms. During this time, the force decreases uniformly from 10³ N to zero as shown in the graph. The change in momentum of the body during this interval is