A 2.0 kg wood block is launched up a wooden ramp that is inclined at a 30˚ angle. The block’s initial speed is 10 m/s. What vertical height does the block reach above its starting point? Use the coefficients μk=0.20 andμs=0.50.

The wood block reaches a height of 4.249 meters above its starting point.

Explanation:

The block represents a non-conservative system, since friction between wood block and the ramp is dissipating energy. The final height that block can reach is determined by Principle of Energy Conservation and Work-Energy Theorem. Let suppose that initial height has a value of zero and please notice that maximum height reached by the block is when its speed is zero.

(1)

Where:

- Maximum height of the wood block, in meters.

- Initial speed of the block, in meters per second.

- Kinetic coefficient of friction, no unit.

- Gravitational acceleration, in meters per square second.

- Mass, in kilograms.

- Distance travelled by the wood block along the wooden ramp, in meters.

- Inclination of the wooden ramp, in sexagesimal degrees.

If we know that , and , then the height reached by the block above its starting point is:

The wood block reaches a height of 4.249 meters above its starting point.

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