Solving a Block's Motion on Inclined & Horizontal Surfaces

In summary, a 3.0 kg block starts at a height of 0.60 m on a plane with a 30 degree angle from the horizontal. After reaching the bottom, it slides along a horizontal surface with a coefficient of friction of 0.20. The net force on the block and its acceleration were found, but the problem can also be solved using the principle of Conservation of Energy. The block gains kinetic energy while coming down, but also loses energy due to friction. The energy at the top equals the energy at the bottom plus the energy lost due to friction. This can be calculated by finding the work done by the force of friction.
  • #1
leighzer
10
0
A block of mass 3.0 kg starts at a height 0.60 m on a plane that has an angle of 30 degrees from the horizontal. Upon reaching the bottom, the block slides along a horizontal surface. If the coefficient of friction on both surfaces is 0.20, how far does the block slide on the horizontal surface before coming to rest?

I found the net force on the block and from there the acceleration, but i think this problem is supposed to be solved using Conservation of Energy theory, or something along those lines.

I know E initial cannot = E final since friction is acting on the block, but I'm not sure how to work that into the problem.

Can anyone help with this question?
 
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  • #2
If I can find the speed of the block at the bottom of the inclined plane, I'll be able to work it out from there, but how do i find the speed when friction is present?
 
  • #3
If you take the block, ramp, floor and the air surrounding all these, the energy will be conserved. But, in this problem, only the block is important. So, while the block's coming down, it gains kinetic energy, but also loses some energy due to friction. You know how much it had initially, this should tell you how much it would have when it is at the bottom of the ramp. The second part is quite simple once you know at what speed the block leaves the ramp.
 
  • #4
So are you saying the energy at the top will equal the energy at the bottom of the ramp?
 
  • #5
If that were so, then the block would not have lost energy.

Energy(top) = Energy(bottom) + Energy(lost)
 
  • #6
Right, but how do you figure out how much energy is lost due to friction? Is it something to do with Work?
 
  • #7
leighzer said:
Right, but how do you figure out how much energy is lost due to friction? Is it something to do with Work?
Exactly. The plane does work on the block. Now, if you know the force due to friction and the definition of work, finding the work done should be simple. :)
 
  • #8
Ok, thanks for the help.
 

Related to Solving a Block's Motion on Inclined & Horizontal Surfaces

1. How does the angle of the incline affect the block's motion?

The angle of the incline affects the block's motion by changing the gravitational force acting on the block. As the angle increases, the component of the force acting parallel to the incline increases, causing the block to accelerate down the incline faster. Conversely, as the angle decreases, the acceleration of the block decreases.

2. What is the difference between static and kinetic friction in regards to a block's motion on an inclined surface?

Static friction is the force that prevents the block from sliding down the incline before it starts moving. Once the block starts moving, kinetic friction comes into play and acts against the motion of the block. This means that the block will continue to move at a constant velocity unless an external force is applied.

3. How does the mass of the block affect its motion on an inclined surface?

The mass of the block does not affect its motion on an inclined surface as long as there are no external forces acting on it. This is because the force of gravity is proportional to the mass of the block, so the acceleration due to gravity is constant regardless of the block's mass.

4. What is the role of the coefficient of friction in the block's motion on an inclined surface?

The coefficient of friction is a measure of the roughness of the surface and determines the amount of friction force acting on the block. A higher coefficient of friction means there is a stronger force resisting the motion of the block, while a lower coefficient of friction means there is less resistance.

5. Can the block's motion on an inclined surface be calculated using Newton's laws of motion?

Yes, Newton's laws of motion can be used to calculate the block's motion on an inclined surface. The force of gravity, normal force, and friction force can be calculated and used to determine the acceleration of the block. This can then be used to calculate the block's velocity and position at any given time.

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