Calculating Minimum Work for a Car on an Incline with Friction

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To calculate the minimum work required to push a 1770 kg car up a 16.2-degree incline with a coefficient of friction of 0.25, the frictional force must be determined first. The normal force (FN) is calculated as 16657 N, leading to a frictional force (Ff) of 4164.25 N. The gravitational force component along the incline is 4839 N. The total force needed to overcome both gravity and friction must be combined to find the total work done. Understanding the relationship between force, work, and energy is crucial for solving this problem accurately.
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Homework Statement



What is the minimum work needed to push a 1770 kg car 346 m up a 16.2 deg incline?
Without friction, I got the the answer of 1670000 J.

What is the minimum work needed if the coefficient of friction is 0.25?

Homework Equations

The Attempt at a Solution



Ff=µFN

FN = 17346 cos 16.2
FN = 16657 N
Ff = .25 * 16657 = 4164.25 N

then, sin16.2 * 17346 = 4839 N

add them? subtract? or is it all completely wrong?
 
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Hello coffeecake,

Try to at least give us your best effort on describing how you've thought through what the steps might be. We're not supposed to offer help unless you've shown that you've given the problem some effort. Things that might be useful in your response: What's the nature dynamic friction? How do you calculate the forces involved in dynamic friction. Can you think of any equations that relate force and work (force and energy)?
 

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