Solve 2 Energy Problems: Conservation of Mechanical Energy

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In summary, the conversation discusses the conservation of mechanical energy in two different scenarios. In the first scenario, a vertical spring with a stiffness constant of 950 N/m is compressed down 0.150m and a 0.30kg ball is released from it. The conversation includes calculations for the upward speed of the ball and the height it will reach. In the second scenario, a ski slides down a 22 degree incline and then along a level surface with a coefficient of friction of 0.090. The conversation involves attempting to solve for the ski's speed at the base of the incline and the distance it will travel along the level surface, using energy methods and free body diagrams.
  • #1
jrd007
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Conservation of Mechanical Energy
(1) A vertical spring (ignore it's mass), whose spring stiffness constant is 950 N/m, is attached to a table and is compressed down 0.150m. (a) What upaward speed can it give to a 0.30kg ball when released? (b) How high above it's orginal position (Spring compressed) will the ball fly?
(a) Okay this is what I did for part a, and my answer was close but not close enough...
1/2kx^2 = 1/2mv^2
.5*950N/m*.150m^2 = .5*.30kg*v^2
v = 8.4 m/s (but the book gave the answer of 8.3 m/s) did I do anything incorrect?
(b) 1/2Kx^2=mgh
.5*950*.150^2 = .3*9.8*h
h = 3.64 m <~~~ I got that one correct.
Law of Conservation of Energy
(2) A ski starts from rest and slides down a 22 degree incline 75 m long.
(a) If the coeffiecent of friction is .090, what is the ski's speed at the base of the incline?
(b) If the snow is level at the foot of the incline and has the same coeffiecent of friction, how far will the ski travel along the level? Use energy methods.
I need some to help me with problem 2. I have drew free bodies already... can't figure out how to attempt it.
 
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  • #2
jrd007 said:
Conservation of Mechanical Energy
(1) A vertical spring (ignore it's mass), whose spring stiffness constant is 950 N/m, is attached to a table and is compressed down 0.150m. (a) What upaward speed can it give to a 0.30kg ball when released? (b) How high above it's orginal position (Spring compressed) will the ball fly?
(a) Okay this is what I did for part a, and my answer was close but not close enough...
1/2kx^2 = 1/2mv^2
.5*950N/m*.150m^2 = .5*.30kg*v^2
v = 8.4 m/s (but the book gave the answer of 8.3 m/s) did I do anything incorrect?
Yes.
You forgot to include a very important type of potential energy in your equation for energy conservation here..

As for 2, what work must be done against the friction?
 
Last edited:
  • #3
A Very important type of PE? Huh? Thereis a missing variable?
 
  • #4
Well, you haven't included the change in GRAVITATIONAL potential energy from when the spring is compressed and when it is not.
 
  • #5
So maybe...

mgh + 1/2kx^2 = 1/2mv^2
(.30kg*9.8*.150m) + (.5*950N/m*.150m^2) = .5*.30kg*v^2
11.1285 = .15 v^2
sqr of 74.19 = 8.61 <~~~ that isn't right...
 
Last edited:
  • #6
I think I may have got it... I believe I added the PE incorrectly. The equation should read:

1/2kx^2 = 1/2mv^2 + mgy

(.5*950N/m*.150m^2) = .5*.30kg*v^2 + (.30kg*9.8*.150m)
10.2465 = .15v^2
sqr of 68.31 = 8.26 = 8.3 m/s

so, that is the correct way?
 
  • #7
(b) 1/2Kx^2=mgh
.5*950*.150^2 = .3*9.8*h
h = 3.64 m

that is correct also?
 

1. What is the principle of conservation of mechanical energy?

The principle of conservation of mechanical energy states that the total amount of mechanical energy in a closed system remains constant over time. This means that the sum of potential energy and kinetic energy in the system remains the same, as long as there are no external forces acting on the system.

2. How is mechanical energy conserved in a closed system?

In a closed system, mechanical energy is conserved because energy cannot be created or destroyed, it can only be transferred from one form to another. This means that as potential energy is converted to kinetic energy, the total amount of mechanical energy in the system remains the same.

3. Can mechanical energy be conserved in an open system?

No, mechanical energy cannot be conserved in an open system because external forces, such as friction or air resistance, can act on the system and cause a decrease in mechanical energy. In an open system, energy is constantly being exchanged with the surroundings, making it impossible for mechanical energy to remain constant.

4. How is mechanical energy related to work and power?

Mechanical energy is related to work and power because work is the transfer of energy from one form to another, and power is the rate at which work is done. In the case of a conservative system, where there are no external forces, mechanical energy is conserved and the work done is equal to the change in mechanical energy.

5. What are some real-world applications of the conservation of mechanical energy?

The conservation of mechanical energy has many real-world applications, such as in the design of roller coasters and other amusement park rides. It is also important in understanding the motion of objects, such as a pendulum or a falling object. Additionally, it is used in the development of renewable energy sources, such as hydroelectric power, which harnesses the energy of falling water to generate electricity.

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