How much work and how much force do we use in pushing a box

[mmoadi]

Homework Statement

How much work do we do when we pull a wooden block with a mass m = 1 kg and we displace it for ∆x= 1 m. The object is being pulled on a rough surface with a coefficient of friction µ_k = 0.1. We are pulling the object with a string; the angle between the string and the surface is 30º. How much strength are we using when pulling the wooden block if the block is moving at 1 m/s at all times.

Homework Equations

F_k= µ_kN
F=ma
N= mg-Fsinθ
W= F∆x

The Attempt at a Solution

→

1) How much work is done:

F_k= µ_kN → F_k= µ_kmg= 0.98N
W= F∆x= 0.98J

2) How much strenght are we using:

W= F∆xcosθ
F= W/ ∆xcosθ= 1.12N

 

[Delphi51]

Those look good. You might check 2 again - for .98/cos(30) I get 1.13 instead of 1.12.

 

[mmoadi]

Yes, you are right, it is 1.13 N.

Thank you for your help! Have a nice day!