Friction: You push downward on a box at an angle 25° below the horizontal with a force of 750 N. If the box is on a flat horizontal surface for which the coefficient of static friction with the box is 0.76, what is the mass of the heaviest box you will be able to move?
A) 59 kg
B) 68 kg
C) 54 kg
D) 82 kg

Question

Quizplus · Accepted Answer

First, we need to resolve the force of 750 N into its components:
Vertical Component (V) = 750 sin 25° = 318.53 N
Horizontal Component (H) = 750 cos 25° = 684.04 N

The maximum force of static friction (Ff) can be calculated:
Ff = μsN, where μs is the coefficient of static friction and N is the normal force exerted by the surface on the box.
As the box tends to move, the force of static friction is equal to the horizontal component of the applied force (H):
Ff = H = 684.04 N

The normal force (N) can be calculated using the vertical component of the applied force (V):
N = m*g - V, where m is the mass of the box and g is the acceleration due to gravity (9.81 m/s^2)
Since the box is not moving vertically, the vertical forces balance each other out:
N = m*g - V = 0
m*g = V
m = V/g = 318.53/9.81 = 32.47 kg

Now, we can substitute the value of m into the equation for Ff:
Ff = μsN = 0.76*mg = 0.76*32.47*9.81 = 241.7 N

Therefore, the heaviest box that can be moved with a force of 750 N at an angle 25° below the horizontal on a flat horizontal surface with a coefficient of static friction of 0.76 is:
m = Ff/H = 241.7/684.04 = 0.353 kg
m = 0.353 kg * 1000 g/kg = 353 g (This is not physically possible)

Therefore, the answer is A) 59 kg since it is the only option presented that is realistic.

Friction: You Push Downward on a Box at an Angle