Question

You push a box a certain distance on a surface with a certain amount of friction. How much more or less work would it be to push a box with three times the mass, twice the distance, and one fifth the amount of friction? Would the amount of work change if you took a meandering path between the two points? Why or why not?

Answer 1

In the initial condition -

Suppose, m = mass of the box

d = displacement

mu = coefficient of friction

So, work done W1 = (mu*m*g)*d

Now in the second condition, the work done W2 = (mu/5)*(3m)*g*(2d) = 1.2*(mu*m*g)*d

So, in the second case, more work will be done.

And percentage of more work = [1.2*(mu*m*g)*d - (mu*m*g)*d] x 100 / (mu*m*g)*d = 20%

Second Part -

Since amount of work done, W = force x displacement

So, by following a meandering path, displacement will be the same.

So, amount of work change in both the cases will be the same.