You are helping a friend move into a new apartment. A 50 kg box needs to be move

Question

You are helping a friend move into a new apartment. A 50 kg box needs to be moved to make room for a couch . You are taller than the box, so you reach down to push it at an angle of 30 degrees from the horizontal. The coefficient of static friction between the box and the floor is 0.50 and the coefficient of kinetic friction between the box and the floor is 0.30

a) If you want to exert the minimum force necessary , how hard would you push to keep the box moving across the floor?

b) Suppose you bent your knees so that your push were horizontal. How hard would you need to push to keep the box moving across the floor?

Explanation / Answer

here,

mass of crate , m = 50 kg

theta = 30 degree

us = 0.5 , uk = 0.3

a)

let the minimum force be F

normal force , N = m * g + F * sin(theta)

N = 50 * 9.8 + F * sin(30)

and

for the block to move

us * N - F * cos(theta) = 0

0.5 * (50 * 9.8 + F * sin(30)) - F * cos(30) = 0

F = 397.7 N

the minimum force applied is 397.7 N

b)

when theta = 0

let the minimum force be F

normal force , N = m * g

N = 50 * 9.8 = 490 N

and

for the block to keep moving

uk * N - F * cos(0) = 0

0.3 * 490 - F = 0

F = 147 N

the minimum force applied is 147 N

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