Work/Conservation of Mechanical Energy

In summary, the problem involves an 80-N box being pulled 20m up a 30 degree incline with an applied force of 115 N. The coefficient of kinetic friction is 0.22. To find the change in kinetic energy, one must first determine the initial and final kinetic energy and then find the difference between the two. This can be done by calculating the work done against friction and the difference in potential energy. It is important to draw a free body diagram and find the net force responsible for motion along the ramp.
  • #1
oceanscreams
1
0

Homework Statement


An 80-N box is pulled 20m up a 30 degree incline by an applied force of 115 N that points upward, parallel to the incline. If the coefficient of kinetic friction between box and incline is 0.22, calculate the change in the kinetic energy of the box.

Homework Equations


ΔKE = 1/2mVf2-1/2mVi2 = mghi- mghf

The Attempt at a Solution


This is what i have understood so far, if there's a mistake please help me.

Given:
Fg= 80N so m=8.15kg
hi= 20m
θ= 30°
μk= 0.22
Fapp= 115N

I drew the ramp, and labeled all the forces. Also, I found Fgx to be 40N. My question is, what do they mean by change in KE? Should I find work done? If so, is it Wnet= Fdcosθ ? I'm really confused, I've spent more than an hour looking for solutions online, but I don't understand the explanation and I decided to try asking myself. Please explain what I should do, I've tried solving several times, but I can't seem to find the answer, and I also have a lot of other problems to solve.

Help is appreciated. Thank you
 
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  • #2
What is the initial kinetic energy?
What is the final kinetic energy?
The difference is the change in kinetic energy.

Can you list all types of energy involved? Where does the box gain energy, where does it lose energy?
oceanscreams said:
Wnet= Fdcosθ ?
You did not introduce d. The formula can be relevant but I would choose a different approach.
 
  • #3
oceanscreams said:
I drew the ramp, and labeled all the forces. Also, I found Fgx to be 40N. My question is, what do they mean by change in KE? Should I find work done? If so, is it Wnet= Fdcosθ ? I'm really confused, I've spent more than an hour looking for solutions online, but I don't understand the explanation and I decided to try asking myself. Please explain what I should do, I've tried solving several times, but I can't seem to find the answer, and I also have a lot of other problems to solve.

actually you should draw a free body diagram and find the net force which will be responsible for motion along the ramp-in up direction.then you can calculate the acceleration - one can assume initial kinetic energy to be zero and the potential energy change will be due to displacement along the ramp -
 

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

The law of conservation of mechanical energy states that the total amount of mechanical energy (the sum of kinetic and potential energy) in a closed system remains constant over time, regardless of any internal changes within the system.

2. How is mechanical energy conserved in a system?

Mechanical energy is conserved in a system when there are no external forces acting on the system, such as friction or air resistance. This means that the total mechanical energy at the beginning of a process is equal to the total mechanical energy at the end of the process.

3. Can mechanical energy be converted from one form to another?

Yes, mechanical energy can be converted from one form to another. For example, potential energy can be converted into kinetic energy when an object falls, and vice versa when an object is lifted.

4. How does the conservation of mechanical energy affect machines?

The conservation of mechanical energy affects machines by limiting their efficiency. Some mechanical energy is always lost due to friction and other factors, so machines cannot convert all of the input energy into useful work. However, by minimizing these energy losses, machines can still be designed to be highly efficient.

5. What are some real-life examples of the conservation of mechanical energy?

Some real-life examples of the conservation of mechanical energy include a pendulum swinging back and forth, a roller coaster going up and down hills, and a ball bouncing on the ground. In all of these cases, the total mechanical energy of the system remains constant, even as the energy is converted between potential and kinetic forms.

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