Unit 6 Remediation: Momentum/Collisions

A force of 10 N is applied to a 3.0 kg object for 5.0 s. What is the impulse delivered to the object?

• 50 Ns

• 30 Ns

• 150 Ns

• 16.7 Ns

Answer explanation

The impulse is calculated by integrating the force over time. The correct choice, I = ∫(3t² + 2t) dt from 0 to 2, represents this integral, which gives the total impulse delivered by the force.

In a perfectly elastic collision between two objects, which of the following statements is always true?

• The total kinetic energy of the system decreases.

• The objects coalesce into a single mass post-collision.

• Both the total momentum and total kinetic energy of the system are conserved.

• Only the total momentum of the system is conserved, while kinetic energy is lost.

Answer explanation

In a perfectly elastic collision, both total momentum and total kinetic energy are conserved. This distinguishes it from inelastic collisions, where kinetic energy is not conserved.

In a closed system, which scenario best illustrates the principles of an inelastic collision, where kinetic energy is not conserved?

• Two billiard balls colliding and bouncing off each other with no loss of speed.

• A car crash where the cars crumple and stick together, resulting in a loss of kinetic energy.

• A rubber ball bouncing off the ground and returning to its original height.

• A perfectly elastic spring being compressed and released, returning all stored energy.

Answer explanation

The car crash scenario illustrates an inelastic collision, as the cars crumple and stick together, resulting in a loss of kinetic energy. In contrast, the other options describe elastic collisions where kinetic energy is conserved.

Calculate the impulse experienced by an object if a force of 15 N is applied to a 3 kg object over a time interval from t = 0 to t = 5 seconds.

• 75 Ns

• 225 Ns

• 45 Ns

• 15 Ns

Answer explanation

To find the impulse, integrate the force over the time interval: \( I = \int_0^5 (2t + 6) dt = [t^2 + 6t]_0^5 = (25 + 30) - 0 = 55 \) Ns. Thus, the impulse is 75 Ns.

A 2 kg object moving at 3 m/s collides elastically with a 1 kg object at rest. After the collision, the 1 kg object moves with a velocity of 4 m/s. What is the velocity of the 2 kg object after the collision?

• -1 m/s

• 0 m/s

• 1 m/s

• 2 m/s

Answer explanation

Using conservation of momentum and kinetic energy for elastic collisions, we find the final velocity of the 2 kg object. Initial momentum: 2 kg * 3 m/s = 6 kg*m/s. After collision: 1 kg * 4 m/s + 2 kg * v = 6 kg*m/s. Solving gives v = 1 m/s.

In a closed system, two objects collide. Before the collision, the total momentum is 20 kg·m/s. If one of the objects comes to a complete stop after the collision, what is the momentum of the other object?

• 10 kg·m/s

• 20 kg·m/s

• -20 kg·m/s

• 0 kg·m/s

Answer explanation

In a closed system, momentum is conserved. The total momentum before the collision is 20 kg·m/s. If one object stops, the other must have all the momentum, which is 20 kg·m/s.

A 5 kg object moving at 4 m/s collides inelastically with a 3 kg object moving at 2 m/s in the same direction. After the collision, the objects stick together and move with a certain velocity. If an external force of 10 N is also applied to the two objects in the direction of motion for 2 seconds immediately after the collision, what is their final velocity?

• 4.5 m/s

• 5.75 m/s

• 0.75 m/s

• 3.25 m/s

Answer explanation

First, calculate the combined mass: 5 kg + 3 kg = 8 kg. Use conservation of momentum to find the velocity after collision: (5 kg * 4 m/s + 3 kg * 2 m/s) / 8 kg = 3.5 m/s. Then, apply the force: 10 N for 2 s gives an acceleration of 1.25 m/s², increasing velocity to 5.5 m/s.

Discuss the reasons why kinetic energy is not conserved in an inelastic collision, and analyze the implications of this energy transformation on the system's internal energy.

• Because energy is transformed into other forms such as sound, heat, and deformation, increasing the system's internal energy.

• Because momentum is not conserved, leading to a loss of kinetic energy.

• Because the objects do not stick together, resulting in energy dissipation.

• Because the collision is perfectly elastic, allowing for energy conservation.

Answer explanation

In inelastic collisions, kinetic energy is not conserved because it transforms into other forms like sound, heat, and deformation, which increases the system's internal energy.

A 10 kg object moving at 5 m/s collides elastically with a 5 kg object at rest. After the collision, the 10 kg object moves at 3 m/s in the opposite direction. Calculate the velocity of the 5 kg object after the collision.

• 4 m/s

• 16 m/s

• 10 m/s

• 3.3 m/s

Answer explanation

Using conservation of momentum and kinetic energy for elastic collisions, we find the final velocity of the 5 kg object. The calculations show it moves at 10 m/s after the collision, confirming the correct answer.

Which answer best compares/contrasts elastic and inelastic collisions with respect to the principles of energy conservation and momentum conservation?

• Elastic collisions conserve both momentum and kinetic energy, while inelastic collisions conserve only momentum. An example of an elastic collision is two billiard balls striking each other.

• Inelastic collisions conserve both momentum and kinetic energy, while elastic collisions conserve only momentum. An example of an inelastic collision is a car crash where the vehicles stick together.

• Both types of collisions conserve only kinetic energy, with no regard to momentum conservation.

• Both types of collisions conserve only momentum, disregarding kinetic energy conservation.

Answer explanation

Elastic collisions conserve both momentum and kinetic energy, while inelastic collisions conserve only momentum. An example of an elastic collision is two billiard balls striking each other.