How Do You Calculate Forces on a Sled on a Slope?

[ccmetz2020]

Homework Statement

A sled weighing 100 N is held in place on a frictionless 20 degree slope by a rope attached to a stake at the top. The rope is parallel to the slope. Use the FBD diagram of the sled below to answer the following. What is the correct formula in both the x and y direction? (referring to F=ma and F=0, Newton's 1st and 2nd laws). What is the normal force of the slope acting on the sled? (HINT: the force of weight is at an angle to your tilted coordinate system and needs to be broken down into its x and y components.)

I have attached the given FBD to this post

Homework Equations

Fy=0
Fx=0?

The Attempt at a Solution

In the y direction:
Fy=0 so
n - Wy = 0
In order to find Wy, I formed a right triangle with the 20 degree angle and used calculated that -100sin20 = approx. -34 N
That makes n = +34 N, right?
In the x direction:
I'm not sure about this but I assume that the net force is equal to zero.
That would mean: T-Wx = 0 right?
In the problem, it does not state to find what tension equals so I think all I had to do was write the correct formula in the x direction. Does this look good to you guys? Thanks.

 

[kjohnson]

It is correct except to find wy it would be 100*cos(20) since the angle is measured relative to the verticle. Likewise wx would be caculated using the sine function.

 

[kerimek]

I would like to clarify a few things about your solution. First, the correct formula in both the x and y direction would be F=ma, which is Newton's Second Law. This law states that the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, since the sled is not moving, the net force must be equal to zero (F=0). This leads to the equations you have correctly written for the y and x direction.

In the y direction, the normal force (n) and the weight (Wy) are balanced, which is why n-Wy=0. You have correctly calculated Wy using the given information and the trigonometric relationship between the angle and the weight component.

In the x direction, the net force is also equal to zero, which means that the tension in the rope (T) must be equal to the weight component in the x direction (Wx). So, the correct equation would be T-Wx=0. This also makes sense intuitively, as the rope is the only force acting in the x direction and it must balance out the weight component.

Finally, to answer the question about the normal force of the slope acting on the sled, you have correctly calculated the normal force to be 34 N. This is the force exerted by the slope on the sled to balance out the weight component in the y direction.

Overall, your solution looks good and shows a good understanding of the concepts involved. Keep up the good work!