In these examples we will be looking at a block that is sitting on a ramp with a known coefficient of friction and then solving information based on the situation. We can begin by looking at a diagram of how gravitational forces will affect a block sitting on a ramp.
This ramp has an angle of elevation of ϴ and a coefficient of friction of μ.
The gravitational force that pushes into the ramp will be mgcosϴ. This means that we can also know the normal force of the ramp pushing back towards the block which will have the same value but in the opposite direction. The gravitational force pushing into the surface will only be a fraction of what the regular gravitational force would be. Unless of course the ramp is at an angle of 0 degrees. Which is of course, a floor, and is not a great ramp.
Try some practice. Round your answer to the nearest Newton.
The gravitational force that pushes the block down the ramp is mgsinϴ. The entire force of gravity isn’t pushing the block down the ramp, only a fraction of it. Unless of course the ramp is at a 90 degree angle. Which is of course, a wall, also not a great ramp.
Try some practice. Round your answer to the nearest Newton.
The friction force that resists the block sliding down the ramp is μmgcosϴ. This force is going to resist the force mentioned above that is trying to push the block down the ramp. If the friction force is greater than the gravitational force that pushes the block down the ramp, then the block won’t slide.
Try some practice. Round your answer to the nearest Newton.
If the gravitational force that pushes the block down the ramp is greater than the friction force, we know that the block will begin sliding. In order to determine the net force that is pushing the block down the ramp we have to subtract the force of friction from the force pushing the block down the ramp. For the purposes of this practice, we will assume that the coefficient of friction has only one value for determining if the block is sliding and determining acceleration and so our force of friction remains constant.
Try some practice. Round your answer to the nearest Newton.
Once we solve our net force we can then use the equation F=ma to solve the acceleration of the block as it slides down the ramp. Remember that our units for acceleration are m/s². The answer bar doesn’t like superscripts so you can use m/s2. However on your tests don’t forget the correct units for acceleration.
Try some practice. Round your answer to the nearest tenth.
If you are feeling up to the challenge, you can actually combine what you know from kinematics once you have the acceleration of the block to solve the velocity of the block as it reaches the base of the ramp. Your hint in determining which equation to use is that there has been no time given.
Try some practice. Round your answer to the nearest tenth.
If you’ve gotten through all of these there are some extra printable practice sheets that you can use. The practice sheet offers new questions each time you visit.
