Force, displacement, and work

In summary, the problem involves Amadeus pushing a desk with a mass of 94.0 kg on a rough wooden floor with coefficients of static and kinetic friction of 0.800 and 0.620, respectively. By using the equations F=u*mg and F=ma, it is determined that the applied force is 566.92N and the acceleration is 6.03 m/s^2. Using the equation x=xi+vit+1/2at^2, the displacement is found to be 108.7 m. Finally, using the equation W=Fd*cos(theta), the work done by Amadeus on the desk is calculated to be 61617.6 J.
  • #1
terichristine
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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



W f = f*d*cos(theta)
F=ma
F=u*mg



The Attempt at a Solution



I used F=u*mg to find the force to be 736.96N and used that to find the acceleration, F=ma=.128. Now I don't know what to do next. I know I need to find the displacement but I don't know how. The only equation I have is delta x=1/2atsubf^2 which yeilds delta x to be 2.304. 2.304*736.96= 1697.7 which is not the right answer. Thanks.
 
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  • #2


Thank you for your question. Based on the information provided, it seems like you are on the right track. However, there are a few things that need to be clarified in order to find the correct answer.

Firstly, when calculating the force, you have correctly used F=u*mg, but the value of u should be the kinetic friction coefficient, since the desk is already in motion. Therefore, the force should be F=0.620*94.0*9.8= 566.92N.

Next, to find the acceleration, you have correctly used F=ma, but the value of F should be the net force acting on the desk, which is the difference between the applied force and the kinetic friction force. Therefore, the equation should be 566.92=94.0*a, which yields an acceleration of 6.03 m/s^2.

Now, to find the displacement, you can use the equation x=xi+vit+1/2at^2, where xi is the initial position (which can be taken as 0), vi is the initial velocity (which can also be taken as 0 since the desk starts from rest), and t is the time. Therefore, x=0+0*6+1/2*6.03*6^2= 108.7 m.

Finally, to find the work done by Amadeus, you can use the equation W=Fd*cos(theta), where F is the applied force, d is the displacement, and theta is the angle between the force and displacement. In this case, theta is 0 degrees, so cos(theta)=1. Therefore, W=566.92*108.7*1= 61617.6 J.

I hope this helps you in finding the correct answer. If you have any further questions, please don't hesitate to ask. Good luck with your studies!
 

1. What is force?

Force is a vector quantity that is defined as any influence that can cause an object to undergo a change in motion. It has both magnitude and direction, and is measured in units of Newtons (N).

2. What is displacement?

Displacement is a vector quantity that refers to an object's change in position or location. It is measured in units of meters (m) and can be positive, negative, or zero depending on the direction of the movement.

3. How is work calculated?

Work is calculated by multiplying the force applied to an object by the distance the object moves in the direction of the force. The formula for work is W = F x d, where W represents work, F is the force, and d is the displacement.

4. What is the relationship between force, displacement, and work?

The relationship between force, displacement, and work is described by the work-energy theorem, which states that the work done on an object is equal to the change in the object's kinetic energy. This means that the more force applied to an object, the greater its displacement and the more work is done on the object.

5. How do different types of work affect an object's energy?

Different types of work, such as mechanical, electrical, or thermal work, affect an object's energy in different ways. Mechanical work, for example, causes a change in an object's kinetic or potential energy. Electrical work can change an object's electrical energy, and thermal work can change an object's thermal energy. However, according to the law of conservation of energy, the total energy of an isolated system remains constant, so the total amount of work done on an object will not change its total energy.

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