A person is trying to drag a box with a mass of 30 kg on a flat floor using a rope attached to it. The static frictional coefficient between the box and floor is 0.50. The angle between the horizontal direction and the rope is 30 degrees. What is the minimum force the person needs to have to move the box along the floor?

F = 131.7N

Explanation:

You are given the following parameters.

Mass M = 30 kg

Coefficient of static friction μ = 0.5

Ø = 30 degrees

When the person is trying to drag the box with force F, the static frictional force Fs will be acting in the opposite direction.

From the figure attached, resolve all forces into horizontal component and vertical component.

Horizontal component:

Fs - F cosØ = 0

Fs = F cosØ

F cosØ = μN ...... (1)

Vertical component:

N + F SinØ - mg = 0

N = Mg - F SinØ ..... (2)

Substitutes m, g and Ø into the equation 2

N = (30 × 9.8) - F × sin30

N = 294 - 0.5F

Substitute N and coefficient of friction into the equation (1)

F cos30 = 0.5 (294 - 0.5F)

Open the bracket

0.8660F = 147 - 0.25F

Collect the like terms

1.116025F = 147

F = 147/1.116025

F = 131.7 N

Therefore, the minimum force the person needs to have to move the box along the floor is 131.7 N

answer and explanation;

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.