Homework Help: Work-Kinetic Energy Theorem

In summary, at the bottom of a driveway that is 20.0º inclined, an average friction force of 4000 impedes the car's motion so that the car's speed is 3.8 m/s. The length of the driveway is 5.1 m.
  • #1
Porcelain
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Homework Statement


A 2100 kg car accelerates from rest at the top of a driveway that is sloped at an angle of 20.0º with the horizontal. An average friction force of 4000 impedes the car's motion so that the car's speed at the bottom of the driveway is 3.8 m/s. What is the length of the driveway?


Homework Equations



Wnet=Change in Kinetic Energy
KE=.5mv^2
Work=FDcos(theta)

The Attempt at a Solution


FDcos(theta)=.5mv^2(final)-.5mv^2(initial)
4000(2100)(9.8)dcos(20)=.5(2100)(3.8)^2
d= ((3.8)^2/(4000(9.8)cos(20)))
d= Some tiny decimal.
The book answer is 5.1m
Where did i go wrong, and how can i fix it?
 
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  • #2
The net force is not 4000N. It is the force of gravity pulling the car down the hill minus the force of friction. Recalculate with this value of F and you will get the right answer
 
  • #3
I'm still not getting it.
 
  • #4
According to Newton's 2nd law of motion, the net force on an object is given by [tex]\sum F=ma[/tex].
In your equation [tex]W=Fdcos\theta[/tex], F is the same as [tex]\sum F[/tex] in the equation for Newton's 2nd law. In the case of the car on the incline, [tex]\sum F=F_{gravity}+F_{friction}[/tex].

You have everything right accept for the force. In your case, you have [tex]\sum F=F_{friction}[/tex].

All you have to do is figure out what the force of gravity is. Think back to a block sitting on an incline and you had to figure out the forces in the x- and y-directions (Im sure you had to do this at some point). When you calculated the gravitational force in the x- and y- directions you had to take into account the angle of the incline. Try this and you should get the right answer. If not, I will check back in a little while and help you out some more.
 

1. What is the Work-Kinetic Energy Theorem?

The Work-Kinetic Energy Theorem is a fundamental principle in physics that relates the work done on an object to its change in kinetic energy. It states that the net work done on an object is equal to the change in its kinetic energy.

2. How is the Work-Kinetic Energy Theorem derived?

The Work-Kinetic Energy Theorem is derived from the laws of motion, specifically Newton's Second Law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. By combining this with the definition of work, which is force multiplied by displacement, we can arrive at the formula for the Work-Kinetic Energy Theorem.

3. What is the significance of the Work-Kinetic Energy Theorem?

The Work-Kinetic Energy Theorem is significant because it allows us to understand the relationship between work and energy. It is a crucial concept in many areas of physics, including mechanics, thermodynamics, and electromagnetism. It also has practical applications in engineering and technology.

4. Can the Work-Kinetic Energy Theorem be applied to all types of motion?

Yes, the Work-Kinetic Energy Theorem can be applied to all types of motion, including linear, rotational, and oscillatory motion. It is a general principle that applies to any object undergoing a change in velocity.

5. How is the Work-Kinetic Energy Theorem used in real-world situations?

The Work-Kinetic Energy Theorem is used in many real-world situations, such as calculating the energy needed to launch a rocket into space, determining the power output of a car engine, and understanding the energy transfer in a rollercoaster ride. It is also used in designing machines and structures that involve moving parts, such as elevators or cranes.

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