How Fast Does a Block Slide Down a Ramp with Friction?

[vic05]

Homework Statement

Block slides down a 1 meter ramp at a 30 degree angle. The coefficient of kinetic friction is 0.4
what is the block's speed at the bottom of the ramp?

Homework Equations

kineticFriction force = coefficient of friction X normal Force

normal Force = force of gravity + mass*acceleration

The Attempt at a Solution

I've tried the problem but i get stuck of finding the normal force required to find the kinetic friction force. Can someone guide me a little bit please... thank you in advanced

 

[Basic_Physics]

The normal force and the component of the weight of the block need to cancel each other out.

 

[vic05]

solved! the professor gave us a formula but I copied it wrong... just for reference the formula which gave acceleration was a = g[sinO - UkcosO]

 

[Basic_Physics]

Physics not about memorizing formulas, it is about deriving them from first principles, so can you?

 

[Nickie]

I would first analyze the given information and identify the key variables involved. In this case, we have a block sliding down a ramp, with a known angle and coefficient of kinetic friction. The goal is to find the block's speed at the bottom of the ramp.

To solve this problem, we can use the equations for Newton's Second Law of Motion and the Work-Energy Theorem.

First, we can calculate the normal force acting on the block using the equation for normal force: normal Force = force of gravity + mass*acceleration. Since the block is on a ramp, the force of gravity will be acting along the ramp's slope, while the normal force will be perpendicular to the ramp's surface. This means we can use trigonometry to find the components of the force of gravity and then add them together to find the normal force.

Next, we can use the equation for kinetic friction force: kineticFriction force = coefficient of friction X normal Force. With the normal force calculated, we can easily find the kinetic friction force acting on the block.

Finally, we can use the Work-Energy Theorem, which states that the work done on an object by a force is equal to the change in the object's kinetic energy. In this case, the work done by the kinetic friction force will be equal to the change in the block's kinetic energy. We can set up an equation with the known values for work and kinetic energy, and solve for the block's speed at the bottom of the ramp.

In conclusion, to find the block's speed at the bottom of the ramp, we need to use a combination of equations and concepts, including Newton's Second Law of Motion, the Work-Energy Theorem, and trigonometry. By breaking down the problem into smaller parts and using the appropriate equations, we can find the solution.