Exam 9: Linear Momentum and Collisions

In a physics demonstration, two rubber balls are dropped down a tube towards the ground, with the lighter ball behind, and not quite in contact with, the heavier ball. The heavier ball collides with the ground and bounces, then collides with the still descending lighter ball. Assume that all the collisions are elastic. In one such demonstration, the heavier ball has a mass of 500 grams, the lighter one a mass of 100 grams, and they are released 1.00 m above the ground. How high does the lighter ball rise after the two collisions?

A curling stone slides on ice with a speed of 2.0 m/s and collides inelastically with an identical, stationary curling stone. After the collision, the first stone is deflected by a counterclockwise angle of 28° from its original direction of travel, and the second stone moves in a direction that makes a 42° clockwise angle with the original direction of travel of the first stone. What fraction of the initial energy is lost in this collision?

Two objects approach each other with velocities such that the total momentum of the masses is zero kg∙m/s, and undergo an elastic collision. Is the sum of the kinetic energies of each object the same before and after the collision?

Three masses are positioned at the following coordinates: 3.0 kg at (3,2); 4.0 kg at (0,-1); and 5.0 kg at (5,-7). What are the coordinates of the center of mass of the system?

A puck with a mass m₁ = 50.0 g moving at 1.00 m/s approaches a stationary puck with a mass m₂ = 100 g on an air table and they undergo a two-dimensional elastic collision. After the collision, both pucks have identical speeds, but travel in different directions. What is the angle between the original and final paths of m₁?

The net force acting on an object is equal to the rate of change of its momentum.

A curling stone slides on ice with a speed of 1.70 m/s and collides elastically with an identical, stationary curling stone. After the collision, the first stone has a velocity of 0.800 m/s in a direction that makes a counterclockwise angle of 61.9° with its original direction of travel. At what speed and what direction is the second stone traveling after the collision?

A tennis ball undergoes an elastic collision when it hits the ground and bounces up. It is given that the speed of the ball just before it hits the ground is -v₀ and immediately after rebounding it is +v₀. Which of the statements below is true?

When objects stick together after colliding, the collision is completely elastic.

The center of mass of a continuous, uniform object is located at the geometric center of the object.

A 1000-kg helicopter hovers over a forest fire and starts to squirt water downward with a speed of 10 m/s at a rate of 40 kg/s. What is the initial upward acceleration on the helicopter when it first starts to release the water?

In a collision between two unequal masses, how does the impulse imparted to the smaller mass by the larger mass compare with the impulse imparted to the larger mass by the smaller one?

In a one-dimensional elastic collision of two identical masses, the masses exchange velocities.

A 2.00-g bullet traveling at 700 m/s hits and becomes embedded in a stationary 5.00-kg wood block. What is the speed of the block immediately after the bullet has stopped moving relative to the block?

A 50.0-kg person stands on a 200-kg raft, which is at rest. She starts to walk on the raft with a speed of 3.00 m/s with respect to the raft. What is the speed of the person relative to the water?

Two objects of equal mass are traveling with identical speeds v and collide. After the collision they travel together with a speed v/2. What was the angle between the original velocities?

A water rocket built from a two-liter bottle half-filled with water pressurized with compressed air can develop a thrust of 300 N. At what rate would water have to come out of the rocket to develop that thrust? The jet of water emerging from the bottle has a diameter of 2.20 cm and the density of water is 1000 kg/m³.

A 900-kg car traveling east at 15.0 m/s collides with a 750-kg car traveling north at 20.0 m/s. The cars stick together. What is the speed of the wreckage just after the collision?

In a particle accelerator, protons are fired at a stationary target and collide elastically with the nuclei of the atoms in the target. In one such experiment, a beam of protons is fired with a speed of 2.10 × 10⁷ m/s. The protons that undergo a collision rebound with a speed of 1.68 × 10⁷ m/s. What is the mass of the nuclei that the protons are colliding against?

A photograph of the two-dimensional elastic collision of two particles shows a particle of mass m₁ approaching a stationary particle of mass m₂. As a result of their interaction, the incident particle moves away along a line that makes an angle of 30° with its original path, and the other particle moves away along a line that makes an angle of 30° to the other side of the original path of the incident particle. What is the ratio of the masses, m₁/m₂?