Dana uses a rope to pull a box that weighs 300 N across alevel

surface with constant velocity. The rope makes an angle of 30above

the horizontal and the tension in the rope is 100 N. What isthe

coefficient of friction?

coefficient of friction is 0.346

Explanation:

given data

weight w = 300 N

angle = 30

tension T = 100 N

to find out

coefficient of friction?

solution

we consider here x component in horizontal direction and y component in vertical direction

so if 100 N tension is apply at 30 degree angle so friction is created at backward direction as shown in figure below

so here

we know here vertical force is zero because there is no vertical motion so

sum of vertical force

N + T sin30 - w = 0

here N is vertical upward force an w is weight and T is tension

N = 300 - 100sin30

N = 250 N

and there is horizontal force is zero because no acceleration so

sum of horizontal force

Tcos30 - f = 0

f = T cos 30

f = μN

μ is coefficient of friction and N is vertical upward force

μN = 100 cos 30

μ (250) = 86.6025

μ = 0.346

so coefficient of friction is 0.346