How Fast Must a Block Slide to Circle a Loop After Inelastic Collision?

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How much energy is lost?In summary, the problem involves finding the minimum initial velocity for a block of mass m to collide with a stationary block of mass M and still allow the second block to complete a loop without falling off. The track is frictionless and the collision is assumed to be perfectly inelastic. The key is to consider the forces acting on the masses at the top of the loop and their initial velocity at the bottom.
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Homework Statement


A block of mass m slides along a frictionless track with speed vm. It collides with a stationarty block of mass M. Find an expression for the minimum value of vm that will allow the second block to circle the loop the loop without falling off if the collision is perfect inelastic.


Homework Equations


Uinitial+Kinitial=Ufinal+Kfinal
U=mgh
K=1/2mv^2

The Attempt at a Solution


Since this is a frictionless track, there is no initial kinetic energy, but that is all i really can figure out i am completely lost someone please help!
 

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It is easier to consider this problem backwards: At the top of the loop, the masses are supposed to stay in their track. Which forces act on them? How can they stay in the track, and which velocity do they need?

The masses come from the bottom of the loop. What was their velocity there?

And afterwards, consider the collision.
 

FAQ: How Fast Must a Block Slide to Circle a Loop After Inelastic Collision?

What is a perfectly inelastic problem?

A perfectly inelastic problem is an economic concept that describes a situation in which the quantity demanded or supplied of a good or service does not change in response to a change in price. This means that the demand or supply curve is completely vertical, indicating that the quantity does not change at all regardless of the price.

2. What are some examples of perfectly inelastic goods?

Some examples of perfectly inelastic goods include life-saving medicines, addictive drugs, and essential services such as electricity and water. These goods are necessary for consumers and have no substitutes, so their demand remains constant despite changes in price.

3. How does a perfectly inelastic problem affect the market?

A perfectly inelastic problem can lead to market inefficiency and price instability. Since the quantity demanded or supplied does not change with price, any changes in supply or demand can result in large fluctuations in price. This can make it difficult for producers to determine the optimal price for their goods or services.

4. What factors can cause a perfectly inelastic problem?

Factors that can cause a perfectly inelastic problem include a lack of substitutes for a good or service, a lack of time to adjust to price changes, and government regulations that limit competition. Additionally, goods that are considered necessities or have high brand loyalty may also exhibit perfectly inelastic demand.

5. How can a perfectly inelastic problem be addressed?

One way to address a perfectly inelastic problem is through government intervention, such as implementing price controls or subsidies. Another approach is to increase competition in the market by promoting the development of substitutes for the good or service. Additionally, educating consumers about the availability of substitutes and the importance of considering price when making purchasing decisions can also help mitigate the effects of a perfectly inelastic problem.

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