How is work calculated with a variable force?

In summary, the question is asking about the work done by a variable force which is given by F = (1.4*10^4N/m)x for 0<x<.21m and then a constant force of 2940N for larger x. The work done in moving the block from x=0 to x=0.30m can be found by splitting the range and calculating the work done for each part separately. Similarly, the work done in moving the block from x=0.10m to x=0.40m can also be calculated by splitting the range and adding the individual work done for each part. The formula for calculating the work done involves an integral.
  • #1
matt@USA
25
0

Homework Statement


A block is acted on by a force that varies as (1.4*10^4N/m)x for 0<x<.21m , and then remains constant at 2940N for larger x. How much work does the force do on the block in moving it from x= 0 to x= 0.30m? How much work does the force do on the block in moving it from x= 0.10m to x= 0.40m?



Homework Equations






The Attempt at a Solution


I am not understanding the question or something. Can someone help me with the equation?
 
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  • #2
matt@USA said:

Homework Equations


Well how would you find the work done with a variable force? (hint: it has an integral in it)

Essentially, the question is telling you that for 0<x<.21 m the force is F = 1.4(104)x and for x>0.21 m, F=2940.

When you get the formula you will need to see what the force will be for the range of x=0 to x=0.4 m. Not that you can split the range as so:


x = 1 to x=4 is the same as x=1 to x=2 + x=2 to x=4.
 

1. How do you calculate the net force when dealing with variable forces?

The net force can be calculated by adding all the individual forces acting on an object together. In the case of variable forces, the forces may change over time, so you will need to calculate the net force at different points in time and then find the average.

2. Can variable forces affect an object's acceleration?

Yes, variable forces can affect an object's acceleration. If the net force on an object changes over time, the object's acceleration will also change accordingly.

3. How do you graph variable forces?

To graph variable forces, you will need to plot the force values on the y-axis and the corresponding time values on the x-axis. This will show how the force changes over time and can help visualize the net force and its effects on an object.

4. What are some common examples of variable forces in the real world?

Some common examples of variable forces include the force of gravity on a falling object, the force of friction on a moving object, and the force of air resistance on a falling parachute.

5. How do variable forces impact the motion of an object?

Variable forces can impact the motion of an object by changing its speed, direction, or both. If the net force is zero, the object's motion will remain constant. However, if the net force is not zero, the object's motion will change accordingly.

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