Physics Forces Question

Question

A 4.5-kg block rests on a rough horizontal table with a rope attached to it. The coefficient of static friction between the block and the table is 0.400 and the coefficient of kinetic friction between the block and the table is 0.380. The rope is pulled at an angle of 35.0◦ above the horizontal. What is the hardest you can pull on the rope while the block remains stationary on the table?

Answer 1

Hi Heather,

In most if not all of physics questions we need to draw the problem. This is a forces problem so draw and then think about all of your forces and put them in the drawing.

µ_sF_n ⁄| F_p

Λ /

|_ _/ θ = 35^ο

<--µ_k F_n

-|-------------------------------------

V

mg

Hey I did my best with the drawing :) hope you get it!

there are 4 forces

1- the weight of the block = mg

2- the static friction force = µ_sF_n

3- the pull force F_p

4- the kinetic friction force always in the direction opposite to motion = µ_k F_n

F_n = mg

we need to factor F_p using θ ,

the horizontal = Fp cos θ to the right

and the vertical = Fp sinθ to the top or against gravity

now the trick to solve is to understand the ask: the hardest pull before the object moves.

at this point we need to focus on the horizontal forces because these are the forces in the direction of motion:

at this instance the two opposite horizontal forces are equal: Fp cos θ = µ_k mg

solve for F_p requires knowing 'm' which is luckily given :) m= 4.5 kg

Fp = 0.38 * 4.5 * 9.8 / cos(35) = 20.46 N

If you liked my explanation give me a five star ;)