Overcoming Friction

Question

Let's say a box is moved by attaching a rope to it and pulling with an applied force at a certain angle. Now, let's say that this is being done on an inclined ramp. How would I find the acceleration?

The mass, coefficient of friction, and applied force are known.

The problem I am having is the fact that this is being done on an inclined ramp. For example, if the box was being pulled on flat ground, then $\Sigma$$Fy$ would be 0 due to the condition of equilibrium. From that the normal force can be found, which in turn can find the force of kinetic friction, and finally the acceleration.

However, if this is done on an inclined ramp, the above would not work. What do I need to do differently to solve this type of problem?

Answer 1

The inclination of the ramp doesn't change a thing except perspective.

As you approach a problem, you have the freedom of defining the axes any way you like - as long as they are at a right angle with each other. An intuitive choice of axes for this problem would be an x-axis that goes parallel to the ramp's surface and a y-axis that goes perpendicular to it.The normal force, for example, is now directed right along the y-axis. Now you need to project all the forces on these axes to get their x and y components. This involves some simple trigonometry, but if you could do it on a flat floor, this is the exact same process. Now, summing all the forces' components on the y-axis should be equal to zero to maintain equilibrium. Summing all of the forces' components on the x-axis and dividing by the mass would give the acceleration of the object up/down the ramp.

Hope this helps!