Why Do Two Different Inclined Planes Yield the Same Final Speed for a Mass?

In summary, the problem involves two fixed inclined planes, ABC and DGEF, with AB=DE=y and BC=EF=x. The coefficient of friction between the wedges and the mass m is \mu. A small mass M is released from point A and reaches the bottom with a speed V1, while the same mass is released from point D and reaches F with speed V2. The question is which option is correct: V1>V2, V1<V2, or V1=V2. The solution involves considering the work dissipated by friction, which can be expressed in terms of x and y without needing the angles.
  • #1
chaoseverlasting
1,050
3

Homework Statement


There are two fixed inclined planes as shown (ABC and DGEF). AB=DE=y, BC=EF=x. The coeff of friction between the wedges and the mass m is [tex]\mu[/tex].

A small mass M is released at the point A and reaches the bottom with a speed V1. The same block is released from point D and reaches F with speed V2. Which is the correct option:

V1>V2
V1<V2
V1=V2.


The Attempt at a Solution



I thought since the potential energy is same here in both cases, but the path length DGF is greater than AC, therefore more energy must be dissipated by friction and so V1>V2.

But the answer is V1=V2.

How?
 

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  • #2
While the path lengths are different, so are the frictional forces, which depend on the angle. Figure out the work dissipated in each case.
 
  • #3
But the angles arent given
 
  • #4
chaoseverlasting said:
But the angles arent given
You don't need the angles--everything you need can be expressed in terms of X & Y.

chaoseverlasting said:

Homework Statement


There are two fixed inclined planes as shown (ABC and DGEF). AB=DE=y, BC=EF=x.
I just realized that this description does not match your diagram. In the diagram, you have both triangles with the same height (that would make the problem too easy!). Per your description, the second triangle must be shorter.

What's the correct description of the problem?
 

1. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is dependent on the object's mass and velocity, and can be calculated using the formula KE = 1/2 * m * v^2, where m is the mass and v is the velocity.

2. How is kinetic energy related to friction?

Friction is a force that opposes the motion of an object. As an object moves, it experiences friction which converts some of its kinetic energy into heat energy. Therefore, friction reduces the amount of kinetic energy an object has.

3. What factors affect the amount of friction experienced by an object?

The amount of friction experienced by an object depends on the surface materials, the weight of the object, and the force pushing the object against the surface. Rougher surfaces, heavier objects, and greater force result in more friction.

4. How does kinetic energy affect the movement of objects?

Kinetic energy is responsible for the movement of objects. The greater the kinetic energy, the faster and farther an object can move. This is why heavy objects require more force to move, as they have more kinetic energy to overcome.

5. How is kinetic energy important in everyday life?

Kinetic energy plays a crucial role in everyday life, as it is the energy that allows us to move and do work. It is also used in various technologies, such as in the generation of electricity through wind turbines and in transportation through cars and planes. Understanding kinetic energy is essential for advancements in technology and improving our daily lives.

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