Determine the work as objects moves in straight line

In summary, the conversation discusses determining the work done on an object by a given force as it moves in a straight line. The solution involves calculating the magnitude of the force and the distance traveled, and then using the definition of work to find the final answer.
  • #1
bfusco
128
1

Homework Statement


Assume that a force acting on an object is given by F=axi+byj, where a=2.9 N/m and b=3.9 N/m. Determine the work done on the object by this force as it moves in a straight line from the origin to r=(10.0i +21.5j)

The Attempt at a Solution


i used the given info to calculate the magnitude of the Force. F=2.9(10)+3.9(21.5)=112.9. i then calculated the distance traveled by doing arctan (21.5/10)=23.7. W=FΔx, W=112.9x23.7=2675. which is wrong, apparently the answer is roughly 1000 J.
 
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  • #2
Maybe you should try calculating the work directly from the definition:

W = ∫(0,0(10,21.5) (ax i + by j). (dx i + dy j)

=∫010 ax dx + ∫021.5 by dy

= (a/2) x2|010 + (b/2) y2|021,5

Complete the evaluation and see how that works out for you.
 

Related to Determine the work as objects moves in straight line

1. What is work in physics?

In physics, work is defined as the measure of the energy transfer that occurs when a force is applied over a certain distance.

2. How is work calculated for an object moving in a straight line?

The work done on an object moving in a straight line can be calculated by multiplying the force applied in the direction of motion by the distance the object moves in that direction.

3. What is the unit of measurement for work?

The unit of measurement for work is Joule (J) in the International System of Units (SI). It can also be measured in other units such as foot-pounds (ft-lb) or calorie (cal).

4. What is the difference between work and power?

Work and power are closely related but have different meanings in physics. Work is the measure of energy transfer, while power is the rate at which work is done. In other words, power measures how quickly work is being done.

5. Can work be negative?

Yes, work can be negative if the force applied and the displacement of the object are in opposite directions. This means that the energy is being transferred away from the object instead of towards it, resulting in negative work.

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