A M₁=1000-kg car is on a rough ramp that is inclined at =20 above the horizontal. It is connected by a light cord over an ideal pulley at the top edge of the ramp to a hangingcrate9 mass M₂₎. The cord pulls on the car parallel to the surface of the ramp.

The coefficient of static friction between the Asphalt and the tires is 0.8 and the coefficient of kinetic friction is 0.7.

1) What should be the mass of the crate to be able to pull the car up the ramp? To answer this question, you need to draw a figure for the problem.

• Draw a free body diagram: Show all the forces (such as force of gravity, friction, normal force, and force of tension in the cord) acting on the car.
• Show all the forces acting on the crate
• Resolve the force of gravity to its components.
• The free body diagram should fill the whole page. Label all the force vectors.
• Write the formulas that apply to the problem on a second sheet of paper.
• These formulas should match with the force vectors on your sketch.
• Derive a formula for the mass.
• Substitute the given data in the problem to calculate the mass of the crate.

2) Repeat the above calculation for the following angles between the inclined ramp and the horizontal. Fill the table with your data.

in degrees	20	30	40	50	60
Mass of the crate in kg