Solve the Homework Problem with Work and Energy

In summary, the problem involves Doug pushing a 5.30 kg crate up a 2.20-m-high 20 degree frictionless slope with a constant force of 27.0 N. The question asks for the speed of the crate as it reaches the top of the slope and can be solved using work and energy. Two different approaches are presented, one using conservation of energy and the other considering work done by the force and against gravity. The correct concept is that work done must be equal to the change in kinetic energy, and the potential energy is given by mgh, not mg(h/sin20).
  • #1
Anthonyphy2013
30
0

Homework Statement



Doug pushes a 5.30 kg crate up a 2.20-m-high 20 degrees frictionless slope by pushing it with a constant horizontal force of 27.0 N. What is the speed of the crate as it reaches the top of the slope?

a) Solve this problem using work and energy.



Homework Equations


Wd=delta KE, ke=.5mv^2 and pe=mgh

The Attempt at a Solution


Conservation of energy
W.d=Pe+KE
Fcos20=mg(h/sin20)+.5mv^2
v= 3.9m/s
but I consider another way about the work done
work done = delta KE
work done on force = Fcos20
work done against the gravitational force = mg(h/sin20)
so Work done by force - work done against the gravitational force =Change of KE .
which one is a corrected concept or both make sense. thanks so much.
 
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  • #2
Anthonyphy2013 said:
...Fcos20=mg(h/sin20)+.5mv^2...

This is not correct.
 
  • #3
szynkasz said:
This is not correct.

why is that not corrected ?
Since work done must be equal to delta KE , so we consider workd done on gravitational force is not a conserved work done ?
 
Last edited:
  • #4
Left side of the equation is force, right is energy. Potential energy is ##mgh##, not ##mg\frac{h}{\sin 20^o}##
 
  • #5


Both concepts make sense and can be used to solve the problem. The first concept uses the conservation of energy principle, where the work done by the force pushing the crate up the slope is equal to the change in potential energy (due to the change in height) plus the change in kinetic energy (since the crate starts from rest at the bottom of the slope). This results in the equation Wd=Pe+KE, which can be rearranged to solve for the final speed of the crate.

The second concept involves breaking down the work done into the work done by the applied force and the work done against the gravitational force. This results in the equation Work done by force - work done against the gravitational force =Change in KE. This approach can also be used to solve for the final speed of the crate.

Both approaches are valid and can be used to solve the problem. It is important to understand the underlying principles of work and energy and how they can be applied in different ways to solve problems.
 

FAQ: Solve the Homework Problem with Work and Energy

1. How do work and energy relate to solving homework problems?

Work and energy are closely related concepts in physics. Work is the amount of force applied to an object multiplied by the distance the object moves in the direction of the force. Energy, on the other hand, is the ability to do work. By using the principles of work and energy, we can solve problems involving the motion of objects and the forces acting on them.

2. What is the basic formula for work?

The basic formula for work is W = F * d, where W is work, F is force, and d is distance. This formula only applies when the force and displacement are in the same direction. If they are not in the same direction, we need to use the dot product to calculate work.

3. How is kinetic energy related to work and energy?

Kinetic energy is the energy an object possesses due to its motion. It is calculated using the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity. Kinetic energy is directly related to work, as the work done on an object is equal to its change in kinetic energy.

4. What is the principle of conservation of energy and how does it apply to homework problems?

The principle of conservation of energy states that energy cannot be created or destroyed, only transferred or converted from one form to another. In homework problems involving work and energy, we can use this principle to solve for unknown variables, as the total energy of a system should remain constant.

5. How do I know which equations to use for solving work and energy problems?

It is important to carefully read the problem and identify the given information and what is being asked for. From there, you can use the relevant equations and principles, such as work-energy theorem and conservation of energy, to solve for the unknown variables. It is also helpful to draw diagrams and use units consistently throughout the problem.

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