# Forces on a Ramp: Understanding Fcosθ - mgsinθ = ma

• frownifdown
In summary, the conversation is about a physics problem where the person is struggling with the reasoning behind using the equation Fcosθ - mgsinθ = ma in the x direction. They are looking for clarification on why those specific components are used and suggest drawing a free body diagram to understand it better.
frownifdown
Here is the link to the problem http://imgur.com/9Vnc5Er

Alright, so I already know how to solve this problem, I am just struggling with the why. This is for my physics test, and he posts the answers to these in class assignments so we can review them.

Looking at step 2, we are supposed to use the equation Fcosθ - mgsinθ = ma(in the x direction). Why is this? Is this because those are the x components of the forces? I don't understand where he is getting those from. If you could shed some light on it that would be awesome. Thanks

The x-direction used is clearly along the ramp with positive direction going up along the ramp, I hope you are not confused about how the x-y coordinate system is defined in the given solution. You might want to draw a free body diagram to clear things up. When you take component of forces along the ramp, that is what you'll arrive at.

## 1. What is Fcosθ in the equation Fcosθ - mgsinθ = ma?

Fcosθ is the force acting in the direction parallel to the surface of the ramp. It is also known as the "component of force in the direction of motion".

## 2. What does mgsinθ represent in the equation Fcosθ - mgsinθ = ma?

mgsinθ represents the force of gravity acting on the object along the ramp. It is also known as the "component of force in the direction perpendicular to the surface of the ramp".

## 3. Why is the equation Fcosθ - mgsinθ = ma important?

This equation is important because it helps us understand the relationship between the forces acting on an object on a ramp and its acceleration. It also allows us to calculate the acceleration of the object using known values of force and angle of the ramp.

## 4. How does the angle of the ramp affect the forces acting on an object?

The angle of the ramp affects the forces acting on an object by changing the magnitude of the force of gravity acting along the ramp (mgsinθ) and the force acting parallel to the ramp (Fcosθ). As the angle increases, the force of gravity increases and the force acting parallel to the ramp decreases.

## 5. Can this equation be used for objects on a ramp with friction?

Yes, this equation can still be used for objects on a ramp with friction. However, the force of friction acting on the object would need to be included in the equation as well, making it Fcosθ - mgsinθ - μmgcosθ = ma, where μ is the coefficient of friction.

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