Box and a Spring on on an inclined plane

• ac7597
In summary, a box of mass 30 kg is held in place on a ramp tilted at 13 degrees with coefficients of static and kinetic friction both equal to 0.12. The box is connected to a spring of spring constant 9 N/m at its rest length. When released, the initial force on the box parallel to the ramp is -31.76N, meaning it will move down the ramp. After moving 0.15m, the net force on the box is -30.4N. The box will have to slide a distance of -0.54m before the net force becomes zero and at this point, the box will continue to move in the same direction with a constant velocity.

ac7597

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

ac7597 said:
friction uFn 0
total m(ax) m(ay)=0
Please explain what you mean by the above statements.
ac7597 said:
m(ax)= u(mgcos(theta)) -mgsin(theta) - kx
So far so good. What next?

I set ax=0 because the first question asks for the initial force. I got kx = 31.7N but that answer is wrong.

ac7597 said:
I set ax=0 because the first question asks for the initial force. I got kx = 31.7N but that answer is wrong.
The initial velocity will be zero, but not the initial acceleration. The initial displacement (x) is also zero.

Is the initial force = u(mgcos(theta))- mgsin(theta)?

ac7597 said:
Is the initial force = u(mgcos(theta))- mgsin(theta)?
Yes.

I got -31.76N is that fine?

Ok -31.76N is the answer. I got the correct answer for the net force when the box move 0.15m as -30.4N. I am confused since shouldn’t the kx result in -33.11N ?

ac7597 said:
when the box move 0.15m
Which way? What does that make the value of x?

negative... I see so its +kx

ac7597 said:
negative... I see so its +kx
No, it's -kx, but since x is negative that has a positive value.

thanks