Dr. Miller pulled a wooden crate at a constant accelerationof 1.23 meters per second per second with a forceof 752 newtons at an angle of 22 degrees above the horizontal. The coefficient of kinetic friction between the crate and the floor was 0.347. Find the mass of the crate.

Use the equation Fnet,x = M*a, to solve for M.

Fnet,x is the net force on the crate in the +x direction. That is equal to 752 cos22 - Ff

The friction force Ff is
Ff = (M*g-752sin22)*(0.347)

Put it all together and turn the algebra crank to get M.

To find the mass of the crate, we can use Newton's second law of motion, which states that the net force applied to an object is equal to the mass of the object multiplied by its acceleration.

First, let's calculate the net force acting on the crate.

1. Decompose the applied force into horizontal and vertical components using trigonometry:
- The horizontal component, Fx, is given by F * cos(θ), where F is the applied force and θ is the angle above the horizontal.
- The vertical component, Fy, is given by F * sin(θ).

Therefore, Fx = 752 N * cos(22°) and Fy = 752 N * sin(22°).

2. Calculate the force of friction, Ff, between the crate and the floor by multiplying the coefficient of kinetic friction (μk) by the normal force (Fn).
- The normal force, Fn, is equal to the weight of the crate, which is given by m * g, where m is the mass of the crate and g is the acceleration due to gravity (approximately 9.8 m/s^2).
- The frictional force, Ff, is equal to μk * Fn.

Therefore, Ff = 0.347 * (m * 9.8 m/s^2).

3. Calculate the net horizontal force, Fnetx, by subtracting the force of friction from the horizontal component of the applied force:
Fnetx = Fx - Ff.

4. Use Fnetx and the given constant acceleration to find the mass of the crate:
Fnetx = m * a, where a is the acceleration.

Therefore, m = Fnetx / a.

Let's plug in the values and calculate the mass of the crate.