Work and energy (change in potential)

In summary, parts a and b of the problem have been solved correctly, with the work done by the force being -9.15J and the particle's speed being 2.71m/s. However, there seems to be an error in part c, as the change in potential energy should be zero in a conservative force field. Further clarification may be needed to determine the mistake in the calculation.
  • #1
lemin_rew
27
0

Homework Statement



part a and b are solved(is it correct), but I am not sure how to solve part c.
A single constant force F = (3.02i + 5.45j)N acts on a 3.69kg particle.

a) Calculate the work done by this force if the particle moves from the origin to the point having the vector position r = (1.97i - 2.77j)m

b) What is the speed of the particle at r if its speed at the origin is 3.51m/s?

c)What is the change in the potential energy of the system?

Homework Equations




The Attempt at a Solution


a) F dot r = (3.02i + 5.45j) dot (1.97i +-2.77j) = (3.02x1.97)+(5.45x -2.77)= -9.15J

b)1/2mvi^2 - (F dot r) = 1/2mvf^2
(0.5x3.69kgx3.51^2 - 9.15J = 1/2(3.69kg)vf^2
v= 2.71m/s

c)W= Ek-Eg
-9.15J = 1/2mvf2-1/2mvi2 - Eg
-9.15J = 1/2(3.69kg)(2.71^2-3.51^2) - Eg
Eg= 0.033J
can anyone tell me what I am doing wrong for part c?
 
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  • #2
I think the result you got in part (c) should have been zero. What you actually got looks like rounding error.
I would have thought that the lost KE has all gone into the PE (i.e. total conserved), no? A uniform force field would be conservative.
 

1. What is work?

Work is the measurement of the amount of force needed to move an object a certain distance. It is calculated by multiplying the force applied by the distance the object moves in the direction of the force.

2. What is energy?

Energy is the ability to do work. It comes in many forms, such as mechanical, thermal, and chemical, and can be converted from one form to another.

3. What is the relationship between work and energy?

Work and energy are closely related concepts. Work is the transfer of energy, and when work is done on an object, it gains or loses energy depending on the direction of the force applied.

4. How is potential energy related to work and energy?

Potential energy is the stored energy an object has due to its position or configuration. When work is done on an object, its potential energy can change, either increasing or decreasing depending on the direction of the force applied.

5. How does change in potential energy affect an object's motion?

According to the law of conservation of energy, energy cannot be created or destroyed, only transferred or transformed. When an object experiences a change in potential energy, it will either gain or lose kinetic energy, which affects its motion. For example, an object with a higher potential energy will have a higher velocity when it reaches the bottom of a hill due to the conversion of potential energy to kinetic energy.

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