# A rolling barrel with initial velocity 20 m/s encounters a hill 10m tall to slow it down. 1....

## Question:

A rolling barrel with initial velocity 20 m/s encounters a hill 10m tall to slow it down.

1. State where its angular speed is 0.

2. State where its rotational kinetic energy will be 0.

3. State where its translation kinetic energy will be 0.

4. For each of the two flat surfaces compare the translational kinetic energy, rotational kinetic energy, and potential energy. (State which quantities are greater than or less than the other quantities).

## Energy conservation principle:

The energy conservation principle consists of a physical law that states that if no external forces act on the system, the total energy of the system should conserve. Energy is not created nor destroyed, it only transforms. This means that a system may present energy transformations, but the overall total energy of the system will remain the same. The total energy of a system can be determined by the sum of the total kinetic and potential energy of the system.

$$E_t=K_e+U_e\\ E_t=0.5mv^2+mgh $$

## Answer and Explanation:

#### Part 1):

The angular speed of the barrel will be zero when the barrel stops rotating. This doesn't mean the barrel stops moving, it means that the barrel will stop rotating as energy is exchanged from rotational and translational kinetic energy to potential energy. The point where the rotational kinetic energy of the barrel turns to zero is the point where the angular speed of the barrel is zero.

#### Part 2):

The rotational kinetic energy of the barrel will be zero at the point where the barrel stops rotating. The point where the angular speed of the barrel turns zero.

#### Part 3):

The translational kinetic energy of the barrel will be zero at the top of the hill. This is the point where the barrel stops completely moving and rotating. It's also the point where the potential energy of the system is at its maximum.

#### Part 4):

There's not enough information to compare the quantities as no image has been attached to determine which quantities we should compare. Also, there's no relevant information about the mass and the radius of the barrel.

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