# Box on a Slant with a Pulley#

The figure shows a block of mass $$m_s$$ resting on a $$\theta = {{params.angl}}^\circ$$ slope. The coefficient of static friction between the block and the sloped surface is $$\mu_s = {{params.coef}}$$. The block on the slope is connected to a hanging block of mass $$m_h = {{params.mass}} \rm{kg}$$ via a massless string that passes over a massless, frictionless pulley. Assume $$g = 9.81 \rm{m/s^2}$$.

## Part 1#

What is the force of friction acting on the block on the slope $$f$$? Express your answer in terms of the variables in the question.

Note that it may not be necessary to use every variable. Use the following table as a reference for each variable:

For

Use

$$m_s$$

ms

$$m_h$$

mh

$$g$$

g

$$\mu_s$$

mu

$$\theta$$

theta

## Part 2#

What is the tension in the string $$T$$? Express your answer in terms of the variables in the question.

Note that it may not be necessary to use every variable. Use the following table as a reference for each variable:

For

Use

$$m_s$$

ms

$$m_h$$

mh

$$g$$

g

$$\mu_s$$

mus

$$\theta$$

theta

Use Newton’s second law and your answers to Part 1 and 2 to determine the minimum value of the mass of the block on the slope $$m_s$$ such that the system remains at rest.
Please enter in a numeric value in $$\rm{kg}$$.