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- Homework Statement
- A box of mass M=30 kg sits on a ramp which is tilted at angle 13 degrees. The coefficients of static and kinetic friction between the box and the ramp are both 0.12. The box is connected to a spring of spring constant k=9 Newtons per meter.

Initially, the box is held in place, and the spring is at its rest length.

The box is then released. What is the initial force on the box parallel to the ramp? Use a negative value to mean "down the ramp", and a positive value to mean "up the ramp." (Hint: draw a set of coordinate axes with X running up along the ramp, and Y running up perpendicular to the ramp).

The box starts to slide down the ramp. After it has moved a distance 0.15 meters, what is the net force on the box parallel to the ramp?

How far will the box have to slide down the ramp before the net force on it (parallel to the ramp) becomes zero? Again, use a negative value to mean "displaced down the ramp from the initial position".

At this point, when the net force on the box is zero, how will it move?

- Relevant Equations
- g=9.8m/s^2

**Homework Statement:**A box of mass M=30 kg sits on a ramp which is tilted at angle 13 degrees. The coefficients of static and kinetic friction between the box and the ramp are both 0.12. The box is connected to a spring of spring constant k=9 Newtons per meter.

Initially, the box is held in place, and the spring is at its rest length.

The box is then released. What is the initial force on the box parallel to the ramp? Use a negative value to mean "down the ramp", and a positive value to mean "up the ramp." (Hint: draw a set of coordinate axes with X running up along the ramp, and Y running up perpendicular to the ramp).

The box starts to slide down the ramp. After it has moved a distance 0.15 meters, what is the net force on the box parallel to the ramp?

How far will the box have to slide down the ramp before the net force on it (parallel to the ramp) becomes zero? Again, use a negative value to mean "displaced down the ramp from the initial position".

At this point, when the net force on the box is zero, how will it move?

**Homework Equations:**g=9.8m/s^2

I tried to create a free body diagram of all the forces on the box:

force x y

normal 0 Fn

gravity -mgsin(theta) -mgcos(theta)

friction uFn 0

force of spring -k(x) 0

total m(ax) m(ay)=0

thus: Fn=mgcos(theta)

m(ax)= u(mgcos(theta)) -mgsin(theta) - kx