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?

1. Find Fn

Fn=18N*cos(28)=15.9N

2. Find Forces in Y direction to solve for m
18N*sin(28)+Fn*fs
18N*sin(28)+(15.9N*0.4)-9.8m=0

Ans: m=1.5kg

2. Find Forces in Y direction to solve for m

18N*sin(28)+Fn*fs
18N*sin(28)+(15.9N*0.4)-9.8m=0

The above solution method is incorrect. I assume the intended 18N*sin(28)+(15.9N*0.4) / 9.8 = m.

The forces in the y direction divided by the acceleration would net you 1.511274299 approx mass for the object.

That's the static coefficient of friction for the surface

Where did the 15.9N come from?

Why did the box go on a diet? Because it wanted to become light enough to slide down the wall! But let's calculate its mass instead.

To find the mass of the box, we can use Newton's second law of motion, which states that force equals mass times acceleration. In this case, the force is the applied force, 18 N, and the acceleration is due to gravity, -9.8 m/s^2.

Since the box is held in place, the force of friction must be equal to the applied force. The force of friction is equal to the product of the coefficient of static friction and the normal force. The normal force is equal to the weight of the box, which is the mass of the box times gravity.

Using the equation for force of friction, we can set up the following equation:

μ(static) * (mass * gravity) = applied force

0.40 * (mass * 9.8) = 18

Simplifying the equation gives us:

0.40mass * 9.8 = 18

Dividing both sides by 9.8:

0.40mass = 18 / 9.8

mass = (18 / 9.8) / 0.40

mass = 1.8367 kilograms (rounded to four decimal places)

So, the mass of the box is approximately 1.8367 kilograms. Keep that box from sliding away!

To find the mass of the box, we can use Newton's second law of motion, which states that the force applied on an object is equal to the product of its mass and acceleration.

In this case, we need to determine the force of gravity on the box, as well as the force of friction holding the box in place. Let's break down the given information:

- The force applied on the box directed upward at 28 degrees above the horizontal.
- The coefficient of static friction between the box and the wall is 0.40.
- The coefficient of kinetic friction between the box and the wall is 0.30.

To begin, let's analyze the vertical forces acting on the box. We can break down the applied force into its vertical and horizontal components. The vertical component will counteract the force of gravity, and the horizontal component will contribute to the friction force.

The vertical component of the applied force is given by:
F_vertical = F_applied * sin(theta)
F_vertical = 18 N * sin(28 degrees)

Next, let's determine the force of gravity on the box. The force of gravity can be calculated using the equation:
Force_gravity = mass * acceleration due to gravity

Assuming standard gravity (9.8 m/s^2), we have:
Force_gravity = mass * 9.8

Now, we need to consider the frictional forces acting on the box. The force of friction is given by:
Force_friction = coefficient of friction * normal force

For the box against the wall, the normal force is equal to the force of gravity:
Force_normal = mass * 9.8

The maximum static friction force can be calculated as:
Force_static_friction = coefficient of static friction * Force_normal

If the applied force is less than the maximum static friction force, the box will remain stationary. Once the applied force exceeds the maximum static friction force, the box will start sliding.

In this case, we know that the box remains stationary until the applied force reaches 18 N. This means that the applied force is equal to the maximum static friction force.

So, we have:
F_applied = Force_static_friction

Now, we can substitute the values into the equations and solve for the mass of the box.

1. Calculate the vertical component of the applied force:
F_vertical = 18 N * sin(28 degrees)

2. Calculate the force of gravity:
Force_gravity = mass * 9.8

3. Calculate the normal force:
Force_normal = mass * 9.8

4. Calculate the maximum static friction force:
Force_static_friction = 0.40 * Force_normal

5. Equate the applied force to the maximum static friction force:
18 N = 0.40 * Force_normal

6. Solve for the mass of the box:
mass = 18 N / (0.40 * 9.8)

Calculating this, we find the mass of the box.

where did you get the 0.4??