Question

Find the value of the mass, m, such that the boxes move at constant speed. Assume that there is no friction in the pulley or the surface.
inclined plane = 40
mass 1 = 15.6kg
mass 2 = m

Answer 1

Answer of question #78725 -Physics- Mechanics - Relativity

Find the value of the mass, $m$, such that the boxes move at constant speed. Assume that there is no friction in the pulley or the surface.

inclined plane = 40°

mass 1 = 15.6 kg

mass 2 = m

Input Data:

Mass: $m_1 = 15.6\,kg$;

Inclined plane: $\alpha = 40{}^\circ$;

Solution:

The speed will become constant when the forces are balanced.

Since the job does not exactly determine where the masses $mass1$ and $mass2$ are located, we have 2 solutions:

- When the mass $m$ is hanging on the block:

Tension force through the block: $T = mg$

The tension force created by the mass on the inclined plane is equal to: $T = m_1 g * \sin \alpha$

$$m g = m_1 g * \sin \alpha$$ $$m = m_1 * \sin \alpha = 15.6 * 0.643 = 10\,kg$$

- When the mass $m$ is on an inclined plane:

Tension force through the block: $T = m_1 g$

The tension force created by the mass on the inclined plane is equal to: $T = m g * \sin \alpha$

$$m_1 g = m g * \sin \alpha$$ $$m_1 = m * \sin \alpha$$ $$m = \frac{m_1}{\sin \alpha} = \frac{15.6}{0.643} = 24.3\,kg$$

It is obvious that the mass on the inclined plane should be greater than the one that is thrown across the block.

Answer:

- $m = 10\,kg$, when the mass $m$ is hanging on the block

- $m = 24.3\,kg$, when the mass $m$ is on an inclined plane

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