How Far Will a Mass Travel on a Frictionless Incline After Going Through a Loop?

In summary, the mass starts at the top of a 10 meter incline with an angle of 36 degrees and encounters friction with a coefficient of kinetic friction of .26. After a loop of radius 2 meters, it travels up a frictionless incline at an angle of 33 degrees. If given enough velocity to make it around the loop, the mass will travel 9.18 meters up the second incline. The initial energy can be found using conservation of energy and the speed at the bottom of the incline is 4.9m/s.
  • #1
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Homework Statement


A mass starts at top of incline with a length of 10 meters with an angle of 36 degrees. Incline has friction with a coefficient of kinetic friction of .26. At bottom of incline is a horizontal, frictionless surface which has a loop of radius 2 meters. After loop is a frictionless incline which is inclined at an angle of 33 degrees. If mass is given enough velocity at top of first incline with friction such that it just makes it around loop, how far up second incline will mass travel in meters? Answer is 9.18.

Homework Equations


[tex]\Delta[/tex]E=Wnc

The Attempt at a Solution


h=Lsin[tex]\theta[/tex]
Wnc=Wfk+WFn=-fkL
Ef-Eo=-fkL
Eo=uo+KE
Ef=uf+KEf
 
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  • #2
So using conservation of energy, what is the initial energy? At the bottom of the incline (just before the loop) what is the speed?
 
  • #3
vo=4.9m/s
vf=9.9m/s
 

FAQ: How Far Will a Mass Travel on a Frictionless Incline After Going Through a Loop?

What is conservation of energy?

Conservation of energy is a fundamental law of physics that states that energy cannot be created or destroyed, but can only be transferred or converted from one form to another.

Why is conservation of energy important?

Conservation of energy is important because it helps us understand and predict the behavior of physical systems. It also allows us to find more efficient and sustainable ways to use energy.

What are some examples of conservation of energy?

Examples of conservation of energy include a pendulum swinging back and forth, a roller coaster moving from a high point to a low point, and a person lifting a weight and then releasing it.

How is conservation of energy related to the first law of thermodynamics?

The first law of thermodynamics is a mathematical expression of the principle of conservation of energy. It states that the total energy in a closed system remains constant, and energy cannot be created or destroyed within that system.

Does conservation of energy apply to all types of energy?

Yes, conservation of energy applies to all types of energy, including mechanical energy, thermal energy, electromagnetic energy, and nuclear energy. This is because energy can be converted from one form to another, but the total amount of energy remains constant.

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