Mechanical Energy:Potential, kinect, etc.

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In summary: You don't need to understand the math behind the centripetal force concept in order to solve this problem. All you need to do is find the speed of the sphere when it reaches point B. This can be done using the conservation of energy equation, which is Ep=Ec=m*v²/2. When you solve for v_B, you get v_B=2m/s.
  • #1
Patolord
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Homework Statement



A sphere of mass 2kg is release from point A off the edge of a hole that is represented of as a semi-circle of R=0,2 m.
consider g=10m/s²
What is the force that the ground apply on the sphere when it passes trough point B(bottom of the hole?

Homework Equations


Ep=m*g*h
Ec=m*v²/2
Q=m*v
F=m*a

The Attempt at a Solution


I tried finding the Potential energy of the sphere at point A that is
Ep=2kg*0,2m*10m/s² = 4J
and the weight of the sphere that is 2*10= 20 N
I don't know what to do anymore the velocity at point B i considered 2m/s because of
Ep=Ec=m*v²/2 then V=2m/s
Help?
Image not from actual problem point A would be the left point B where it is on the pic
35c+Stable+Ideal+copy.jpg
 
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  • #2
You can simply find the speed of the sphere when it reaches point B using conservation of energy.Call it [itex] v_B[/itex]. When the sphere is moving in the semi-circle,it needs a centripetal force which at point B is equal to [itex] \frac{mv_B^2}{R} [/itex]. But this centripetal force can be provided only by the circular track and nothing else so your answer is [itex] \frac{mv_B^2}{R} [/itex].
 
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  • #3
AH thanks the answer is 60N i guess you have to sum that with the weight that is 20N
40 +20 =60 N
but i don't get where mv2/r comes .. i don't have that on my theory
they just gave mv²/2 and m*g*h
 
  • #4
You need to understand the centripetal force concepts before solving this problem. You should know that the centripetal force mv^2/r is the net force acting inward toward the center of the circle. So the centripetal force is 40 N inward and is comprised of the net force of the ground normal force acting up
and the weight acting down, the net force
 
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  • #5
Thank you, now i see why couldn't soulve any problems envolving circles xD
 

1. What is mechanical energy?

Mechanical energy is the energy possessed by an object due to its motion or position. It can be divided into two forms: potential energy, which is the energy an object has due to its position or shape, and kinetic energy, which is the energy an object has due to its motion.

2. How is potential energy related to mechanical energy?

Potential energy is a form of mechanical energy. It is the energy that an object has due to its position or shape, and can be converted into other forms of energy, such as kinetic energy, as the object moves or changes position.

3. What is kinetic energy?

Kinetic energy is the energy an object has due to its motion. It is directly proportional to the mass of the object and the square of its velocity. Kinetic energy can be converted into other forms of energy, such as potential energy, as the object slows down or changes direction.

4. How does mechanical energy affect everyday life?

Mechanical energy plays a vital role in our everyday lives. It is responsible for powering machines and vehicles, as well as allowing us to perform physical activities such as walking, running, and lifting objects. It is also used in various forms of energy production, such as hydroelectric power and wind turbines.

5. Can mechanical energy be created or destroyed?

According to the law of conservation of energy, mechanical energy cannot be created or destroyed. It can only be converted from one form to another. This means that the total amount of mechanical energy in a closed system remains constant, even as it is transferred and transformed between different objects and forms of energy.

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