# Find the magnitudes of all of the forces acting on the sled

## Homework Statement

A person pulls on a rope attached to a 5 kg sled. The rope makes an angle of 30 degrees with the horizontal. Sled accelerates horizontally at 1.7 m/s^2. There is no friction.

ma = Fnet
mg = Fgravity

## The Attempt at a Solution

Fnorm = earth force up on sled
Fr = the force of the rope of the sled being pulled

The x and y components for Fr would be y = Frsinθ and x=Frcosθ.
Vector of Fnorm = <0, Fnorm>
Vector of Fg = <0, -50>
Vector of Fr = <Frcos30, Frsin30>

Fnetx => 8.5 = Frcos30
Fnety => 0 = Fc - 50 + Frsin30

So I got this far and starting doing algebraic stuff to solve for Fr and then plugging that into the second equation. From there, I solved for Fc, and the value was 45.095 N. And from the Fnetx equation, Fr = 9.8 N.
However, when I added all the magnitudes of forces, my answer does not equal to the Fnet, which is ma = 8.5 N.
Can someone help me with this? Have I forgotten something? Am I even doing this right?

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Chestermiller
Mentor
Show us how you added up the forces to get the net force. Your answers so far look OK.

Chet

For the net force, I did the force magnitude of Fnorm plus force magnitude of Fr minus the force magnitude of Fg, which is 8.5 N + 45.095 N - 50 N. That answer got me 3.595 N.

Chestermiller
Mentor
For the net force, I did the force magnitude of Fnorm plus force magnitude of Fr minus the force magnitude of Fg, which is 8.5 N + 45.095 N - 50 N. That answer got me 3.595 N.
The forces have to be added as vectors, not as scalars.

Chet

The forces have to be added as vectors, not as scalars.

Chet
How do I do that?

Chestermiller
Mentor
How do I do that?
You do it by adding their components. But, you've already done that.

Chet