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A 10 kg box is traveling 5 m/s down a 4 meter inclined plane

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A 10 kg box is traveling 5 m/s down a 4 meter inclined plane that is at an angle of 37 degrees. The coefficient of friction is .4. What is the change in potential energy, the work done by the friction force and the speed of the box before it reaches the end of the inclined plane.
Submitted: 5 years ago.
Category: Homework
Expert:  akch2002 replied 5 years ago.
Customer: replied 5 years ago.
As soon as possible....
Expert:  akch2002 replied 5 years ago.
I will reply within 10-15 minutes.
Customer: replied 5 years ago.
Thanks
Expert:  akch2002 replied 5 years ago.

A 10 kg box is traveling 5 m/s down a 4 meter inclined plane that is at an angle of 37 degrees. The coefficient of friction is .4. What is the change in potential energy, the work done by the friction force and the speed of the box before it reaches the end of the inclined plane.

Change in potential energy = mgh = mg*4sin 37

= 10*9.8*4*0.6018 = 235.91Joules.

Work done by frictional force = μmgcosθ*distance travelled

= 0.4*10*9.8*cos37*4

= 125.226J

If velocity change at end is v, we have 0.5mv2= mgh

Or v = sqrt(2gh) = sqrt(2*9.8*4sin37) = 6.868m/sec

Hence, velocity at end = 5+6.868 = 11.868m/sec

Kindly ACCEPT the answer. BONUS and POSITIVE feedback will be appreciated.

Customer: replied 5 years ago.
Expert:  akch2002 replied 5 years ago.
Can you inform answer? There seems to be no mistake in my approach.
Customer: replied 5 years ago.
Would you be able to make it clearer? For example, where did you get the formula for the velocity from? Isn't friction a nonconservative force?
Expert:  akch2002 replied 5 years ago.

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Customer: replied 5 years ago.
I thought gravity, elastic spring, and electric are the only conservative forces?
Expert:  akch2002 replied 5 years ago.
Frictional force should be conservative as it is form of gravitational force in this case.
Customer: replied 5 years ago.
How do you figure that out?
Expert:  akch2002 replied 5 years ago.
Because frictional force is μmgcosθ.
Customer: replied 5 years ago.
But why would the textbook list it as a nonconservative force then?
Expert:  akch2002 replied 5 years ago.
Frictional force can appear in many situations. In one situation, it may be conservative and in the other situation,it may be non-conservative.
For solving this problem, it is not required to know whether frictional force is conservative or not.