Conservation of Energy in a Sliding Box on an Incline

In summary, the conversation discusses a physics problem involving a box sliding down an incline plane. The box has a known mass, height, and initial and final speeds. The task is to calculate the mechanical energy lost due to friction. The participants suggest starting by looking at the different forms of energy involved and applying the principle of conservation of energy. They also mention three specific energies to consider: potential gravitational energy, kinetic energy, and work of friction.
  • #1
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Homework Statement



A 1.90 kg box slides down a rough incline plane from a height h of 1.51 m. The box had a speed of 2.99 m/s at the top and a speed of 2.56 m/s at the bottom. Calculate the mechanical energy lost due to friction (as heat, etc.).
 
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  • #2
hi - any ideas on how to go about this? I would start by looking at the differenet forms of energy involved & thinking about conservation of energy
 
  • #3
Welcome to PF. :) Hopefully you'll be wanting to change that username soon enough.

Look at the total initial energy, and at the total final energy, remember that conservation of tells you that they're equal. You have three energies involved in this problem. Potential gravitational energy, kinetic energy and the work of friction, try and see which ones you know for the initial and final states, and which ones you don't.
 

FAQ: Conservation of Energy in a Sliding Box on an Incline

What is the center of mass?

The center of mass is the point at which the total mass of an object is concentrated. It is the average position of all the mass in an object, taking into account the positions and masses of all its individual particles.

How is the center of mass determined?

The center of mass can be determined by finding the weighted average of the positions of all the particles in an object, with the weights being the masses of the particles. This can be calculated using the formula:

xcm = (m1x1 + m2x2 + ... + mnxn) / (m1 + m2 + ... + mn)

where xcm is the x-coordinate of the center of mass and m1, m2, etc. are the masses of the individual particles.

What is the significance of the center of mass?

The center of mass is important in understanding the motion of an object. It is the point at which an external force can act on an object to produce translational motion without causing any rotation. It also helps in determining the stability and equilibrium of an object.

How does the center of mass relate to momentum?

The center of mass is related to momentum because the total momentum of a system of particles is equal to the mass of the system times the velocity of the center of mass. This is known as the principle of conservation of momentum.

Can the center of mass be outside of an object?

Yes, the center of mass can be outside of an object. This is because the center of mass is a mathematical point that represents the average position of all the mass in an object. It does not necessarily have to lie within the physical boundaries of the object.

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