Force, displacement, and work

In summary, the problem involves determining the work done by Amadeus on a desk with a mass of 94.0 kg. The desk is pushed horizontally on a rough wooden floor with a coefficient of static friction of 0.800 and a coefficient of kinetic friction of 0.620. Amadeus pushes with just enough force to get the desk moving and continues pushing for 6.00 seconds. Using the second law of motion, the acceleration is found to be 7.84 m/s^2. Using the kinematic equation for displacement, the desk is found to have moved 141.2 meters in 6 seconds. However, the incorrect coefficient of static friction was used, resulting in a wrong answer.
  • #1
terichristine
2
0

Homework Statement


Amadeus pushes horizontally on a desk that rests on a rough wooden floor. The coefficient of static friction between the desk and the floor is 0.800 and the coefficient of kinetic friction is 0.620. The desk has a mass of 94.0 kg. He pushes just hard enough to barely get the desk moving and continues pushing with that force for 6.00 s. What work does he do on the desk during that time (HINT: Since once movement starts, friction changes to sliding friction, which is less than maximum static friction, the desk will be accelerating. SO, use the 2nd law to find the acceleration, then find out far it went in 6 s...)?


Homework Equations



u*mg
f=ma
w=d*f
D=1/2at^2

The Attempt at a Solution



I used:
u*mg=.8*94*9.8=736.96N
f=ma=736.96/94=acceleration=7.84
and displacement=1/2at^2=(.5)*(7.84)*(6^2)=141.2
w=d*f=141.2*736.96=104059 and that's wrong. I don't know what I am doing wrong. Thanks.
 
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  • #2
terichristine said:

Homework Statement


Amadeus pushes horizontally on a desk that rests on a rough wooden floor. The coefficient of static friction between the desk and the floor is 0.800 and the coefficient of kinetic friction is 0.620. The desk has a mass of 94.0 kg. He pushes just hard enough to barely get the desk moving and continues pushing with that force for 6.00 s. What work does he do on the desk during that time (HINT: Since once movement starts, friction changes to sliding friction, which is less than maximum static friction, the desk will be accelerating. SO, use the 2nd law to find the acceleration, then find out far it went in 6 s...)?


Homework Equations



u*mg
f=ma
w=d*f
D=1/2at^2

The Attempt at a Solution



I used:
u*mg=.8*94*9.8=736.96N
f=ma=736.96/94=acceleration=7.84
and displacement=1/2at^2=(.5)*(7.84)*(6^2)=141.2
w=d*f=141.2*736.96=104059 and that's wrong. I don't know what I am doing wrong. Thanks.

Try using mu k, coefficient of kinetic friction, because the only work done is while the force displacing the box is acting. It said this in the hint. So 0.62 instead of 0.80
 

What is force?

Force is a physical quantity that describes the amount of push or pull on an object. It is measured in Newtons (N) and is represented by the symbol F.

What is displacement?

Displacement is the change in position of an object from its initial to final position. It is a vector quantity, meaning it has both magnitude (size) and direction. It is measured in meters (m) and is represented by the symbol d or Δx.

What is work?

Work is a measure of the energy transferred to or from an object by a force. It is calculated by multiplying the force applied by the distance over which it is applied. It is measured in joules (J) and is represented by the symbol W.

How are force, displacement, and work related?

According to the work-energy theorem, the work done on an object is equal to the change in its kinetic energy. This means that when a force is applied to an object and causes it to move a certain distance, work is done. The amount of work done is directly proportional to the force applied and the displacement of the object in the direction of the force.

What is the difference between work and power?

Work and power are both measures of energy, but they are different concepts. Work is the amount of energy transferred to or from an object, while power is the rate at which work is done. Power is calculated by dividing work by the time it takes to do it. It is measured in watts (W) and is represented by the symbol P.

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