What is the total work required to drive a screw into a block of wood?

In summary, the conversation discusses the relationship between the number of turns needed to drive a screw into wood and the torque required for the task. It is stated that the torque increases linearly with the depth that the screw has penetrated into the wood, and the maximum torque is 12 N m when the screw is completely in the wood. The question asks for the total work (in Joules) required to drive in the screw, and after some discussion, it is determined that the average torque is 6 N m and the work is calculated to be 754 J.
  • #1
smhippe
19
0

Homework Statement


It takes 20 turns to drive a screw completely into a block of wood. Because the
friction force between the wood and the screw is proportional to the contact area between
the wood and the screw, the torque required for turning the screw increases linearly with
the depth that the screw has penetrated into the wood. If the maximum torque is 12 N m
when the screw is completely in the wood, what is the total work (in Joules) required to
drive in the screw?


The Attempt at a Solution


So I tried to do an integral by finding out how much the torque changed per rotation. Then using that as the equation and the total distance turned to be plugged in.
[tex]\int.6x[/tex] from 0 to 7200. I got a very large number and I don't think I did it right...
 
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  • #2
Rather than use calculus, which is bound to throw you off, what is the average torque if it linearly increases? Then what is the definition of Work for a torque acting through one rotation?
 
  • #3
Well, the equation for how it increases is just .6*(rotation number). The average torque would be the maximum and minimum divided by two...The maximum is obviously 12 so would that make the minimum be 0? That doesn't really make sense though. In that case the average would be 6. The equation for work is torque times the rotation distance. This gives 754 J which is the correct answer now that I check it. Thanks Phantom...guess I just needed another person to point me in the right direction!
 

What is the definition of total work done on a screw?

The total work done on a screw is the amount of energy required to rotate the screw and move it through a certain distance. It takes into account both the rotational work and the translational work of the screw.

How is the total work done on a screw calculated?

The total work done on a screw can be calculated by multiplying the force applied to the screw by the distance it is moved. This takes into account both the linear displacement and the angular displacement of the screw.

What factors affect the total work done on a screw?

The total work done on a screw is affected by the force applied, the distance it is moved, the angle at which it is rotated, and the friction between the screw and the surface it is moving on. These factors can increase or decrease the total work done on a screw.

Why is the concept of total work done on a screw important?

The concept of total work done on a screw is important in understanding the efficiency of a screw and how much energy is required to move it. It also helps in designing and optimizing screw systems for various applications.

Can the total work done on a screw ever be negative?

Yes, the total work done on a screw can be negative if the force applied is in the opposite direction of the displacement. This means that the screw is being unscrewed and energy is being released rather than being used to move the screw forward.

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