Work done by a varying force of a block

In summary, the block with a mass of 5.00kg experiences a net force that varies with its position on the x-axis. When x=0, the initial speed of the block is 2.0 m/s. The work done on the block when it is displaced from x=0 to x=8 is 25J, and the final speed at x=8 is 3 m/s. These solutions were obtained by calculating the area under the curve and using the work-energy theorem.
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Homework Statement


A block with mass 5.00kg, moves along the x-axis with zero friction. The block experiences a net force Fx that varies with it's position x. When x=0, v (initial speed) is equal to 2.0 m/s

Find the work done on the block when it is displaced from x=0 to x=8

What is the final speed at x=8

This is not the original problem statement ... I had to translate it to English in order to post it here. :p

Se attached image for the graph of the relationship between the force and displacement.

Homework Equations





The Attempt at a Solution


Calculated the area in the trapezoid, and subtracted the area of the triangle. 30J-5J=25J, I think this is right answer?

Then I used the relation between work and kinetic energy

W=delta K=(1/2)m*v_f^2 - (1/2)m*v_i^2
where the subscript i and f stands for initial and final speed

Solved this for v_f and got the answer 3 m/s

Are these answers correct? Unfortunately, I don't have the answers, since this is a problem I got from my physics professor, not from the textbook.

Thanks in advance. :)
 

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  • #2
Yes, you calculated the area under that curve correctly and applied the work energy theorem (work=change in kinetic energy) to calculate the final velocity at x=8. Everything seems fine to me.
 

FAQ: Work done by a varying force of a block

1. What is work done by a varying force?

Work done by a varying force refers to the amount of energy transferred to a body when a force acts on it and causes it to move a certain distance in the direction of the force. This work can be positive or negative, depending on the direction of the force and the displacement of the body.

2. How is work done by a varying force calculated?

The work done by a varying force can be calculated by multiplying the magnitude of the force by the displacement of the body in the direction of the force. If the force is not constant, the work can be found by taking the integral of the force with respect to the displacement.

3. What is the unit of measurement for work done by a varying force?

The unit of measurement for work done by a varying force is joules (J). This is the same unit used for measuring energy and is equivalent to 1 newton-meter (N∙m).

4. Can work done by a varying force be negative?

Yes, the work done by a varying force can be negative if the force and displacement are in opposite directions. This indicates that the force is acting against the motion of the body, resulting in a decrease in the body's energy.

5. How does the graph of work done by a varying force look like?

The graph of work done by a varying force is a curve, with the force on the x-axis and the work on the y-axis. The shape of the curve depends on the type of force and the displacement of the body. If the force is constant, the graph will be a straight line, but if the force varies, the graph will be a curved line.

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