Question

A 180 lb crate is on the ground, and a strong rope is attached. You need to move it across the basement floor, which has a coefficient of friction of 0.7 against the wood of the crate. To avoid actually working you call your friend to complain that you have to push it so hard. Your friend says you should pull it with the rope (your height will cause it to have a 60° angle to horizontal), since it will lower the weight and therefore the friction force. You counter (still avoiding work) that you will also have less force on the crate so it cancels out. What is the right answer? Is it better to pull with the rope or push? Why?

Answer 1

`F = 505.13 N`

Yes it is better to pull the rope rather than push it

Step-by-step explanation:

Let the force is applied at an angle of 60 degree

so we will have net vertical force on the crate is given as

`F_n + Fsin60 = mg`

here we know

`m = 180 lb`

`m = 81.65 kg`

`F_n = 81.65(9.81) - Fsin60`

`F_n = 801 - 0.866 F`

now friction force on the crate is given as

`F_x = \mu F_n`

`Fcos60 = 0.7(801 - 0.866 F)`

`0.5F + 0.61F = 560.7`

`F = 505.13 N`

Yes it is better to pull the rope rather than push it