A small box is held in place against a rough vertical wall by someone pushing on it with a force directed upward at 28degrees above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30, respectively. The box slides down unless the applied force has magnitude 18 N.
What is the mass of the box in kilograms?
Here's a free-body diagram indicating all forces acting on the box.
http://img142.imageshack.us/img142/7156/leahi.jpg
Summing forces in the x-direction will let you solve for the value of the normal reaction, N.
Using N and the static friction coefficient (since the box has not moved yet), you will be able to find the mass of the box. If I am not mistaken, the mass is around 1.51 kg.
Post if you have questions.
To determine the mass of the box in kilograms, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's analyze the forces acting on the box:
1. The force applied by the person pushing the box upward at an angle of 28 degrees above the horizontal.
2. The normal force exerted by the wall on the box, directed perpendicular to the surface of the wall.
3. The force of gravity acting on the box, directed downward.
To begin, let's resolve the applied force into its vertical and horizontal components.
Vertical component of the applied force = F * sin θ
Horizontal component of the applied force = F * cos θ
θ = 28 degrees
F = 18 N
Vertical component of the applied force = 18 N * sin 28°
Horizontal component of the applied force = 18 N * cos 28°
Next, let's analyze the forces in the vertical direction:
The vertical component of the applied force opposes the force of gravity, so we have:
Vertical component of the applied force - Weight = 0
18 N * sin 28° - m * g = 0
Weight = m * g (mass multiplied by the acceleration due to gravity)
Solving for the mass (m):
m = (18 N * sin 28°) / g
The acceleration due to gravity is approximately 9.8 m/s^2.
Therefore, the mass of the box is:
m = (18 N * sin 28°) / 9.8 m/s^2
Calculating this value will give us the mass of the box in kilograms.