- #1
brentwoodbc
- 62
- 0
Homework Statement
I get an answer of 7.2, it says the answer is supposed to be 6.
I do w=fd
w=(16-4)x(.8-.2)
w=12x.6
w=7.2?
thanks.
Varying force is applied to an object problem
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SUMMARY
The problem involves calculating work done by a varying force applied to an object, where the initial calculation of 7.2 joules is incorrect. The correct approach requires recognizing that the force is not constant and involves integrating the force over the distance. The formula used, w = fd, is insufficient for varying forces; instead, one must sum the contributions of force over small intervals or use calculus to integrate the force function over the specified distance.
PREREQUISITES- Understanding of work-energy principles in physics
- Basic knowledge of calculus, specifically integration
- Familiarity with piecewise functions
- Ability to interpret force-distance graphs
- Learn how to calculate work done by a varying force using integration techniques
- Study piecewise continuous functions and their applications in physics
- Explore graphical methods for approximating integrals, such as Riemann sums
- Review the fundamentals of force and motion to reinforce concepts of work
Students studying physics, particularly those tackling problems involving work and varying forces, as well as educators looking for effective teaching methods in calculus applications.
I get an answer of 7.2, it says the answer is supposed to be 6.
I do w=fd
w=(16-4)x(.8-.2)
w=12x.6
w=7.2?
thanks.
- #2
berkeman
Admin
- 69,537
- 25,119
brentwoodbc said:Homework Statement
I get an answer of 7.2, it says the answer is supposed to be 6.
I do w=fd
w=(16-4)x(.8-.2)
w=12x.6
w=7.2?
thanks.
The force is varying with distance, not a constant diffrerence of the ending and starting force. You will need to add up all the little F*d contributions to get the total work. You could write an equation for the line, the F(d) line, or you could approximate it as a piece-wise continuous stair-step waveform.
If you have used calculus in your course so far, write the equation for the line and do the integration to sum up the F(d) over the interval. If you haven't use integration for this before, just do the sum for each little interval you see on the graph between the endpoints that they are asking about.
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