Polygon Of Forces To Demonstrate Equilibrium

[sperrya]

Homework Statement

Use the polygon of forces to demonstrate that a 200 kg crate on a 25^o incline is in equilibrium on the slope.

Homework Equations

See attached

The Attempt at a Solution

Please see attached for my attempt, I think I am in the right ball park, just need to know what seat to be in, i.e. how do I plot the answer to satisfy the question. Please help...

Thanks

 

[SteamKing]

You must draw the force polygon so that the forces show the correct magnitude and direction. For instance, how must the weight vector of the box be drawn?

 

[sperrya]

Hi there, thanks for your reply, I know I need to draw a force triangle of some sort, but unsure how to do it with the information I have. Even then, is this a correct polygon of force??

Thanks

 

[SteamKing]

What direction is the weight force usually drawn?

 

[rwisz]

for sharing your attempt. It looks like you are on the right track. To demonstrate equilibrium using the polygon of forces, we need to first draw a diagram of the situation. In this case, we have a 200 kg crate on a 25o incline. We can draw a free-body diagram of the crate, showing all the forces acting on it. These forces include the weight of the crate (200 kg * 9.8 m/s^2), the normal force from the incline, and the force of friction.

Next, we can draw a polygon of forces, starting with the weight of the crate as the first force. From there, we can add the normal force and the force of friction in the appropriate directions and magnitudes. The polygon should close, indicating that the forces are in equilibrium.

To plot the answer, we can use a protractor to measure the angle of the incline and use a ruler to measure the length of each force vector. Then, we can use a scale (1 cm = 100 N) to accurately plot the forces on a graph paper.

To satisfy the question, we need to show that the polygon of forces closes, indicating that the forces are in equilibrium. We can also calculate the net force acting on the crate by adding all the forces together. If the net force is equal to zero, then the crate is in equilibrium. We can also calculate the torque (or moment) of all the forces about a point on the incline to further demonstrate equilibrium.

I hope this helps. Good luck with your homework!