fred and barney are pushing a 200 kg crate up a plank, they have to put it on a roller. they apply a force of 1600N to the crate in order to accelerate at .5 m/s^2. the angle of the plank is 20 degrees. find the coefficient of friction.

Forces down the ramp:

m g sin 20
mu m g cos 20

Force up the ramp
1600 N
so
1600 - m g sin 20 - mu m g cos 20 = m (.5)

is the coefficent .16?

To find the coefficient of friction, we can start by calculating the net force acting on the crate.

1. Determine the parallel and perpendicular components of the applied force:
- The parallel component of the force is given by F_parallel = F_applied * sin(angle).
- The perpendicular component of the force is given by F_perpendicular = F_applied * cos(angle).

2. Calculate the gravitational force acting on the crate:
- The gravitational force is given by F_gravity = m * g, where m is the mass of the crate and g is the acceleration due to gravity. In this case, m = 200 kg and g = 9.8 m/s^2.

3. Determine the net force acting on the crate in the direction of motion:
- The net force is given by F_net = F_parallel - F_friction, where F_friction is the force of friction opposing the motion.

4. Apply Newton's second law of motion to relate the net force to acceleration:
- F_net = m * a, where a is the acceleration. In this case, a = 0.5 m/s^2.

5. Solve for the force of friction:
- F_friction = F_parallel - F_net.

6. Finally, calculate the coefficient of friction:
- The coefficient of friction is given by the equation: frictional force = coefficient of friction * normal force.
- The normal force is equal to the perpendicular component of the applied force, which is F_perpendicular.
- Therefore, the coefficient of friction can be calculated as: coefficient of friction = F_friction / F_perpendicular.

Now, let's calculate the coefficient of friction step by step:

Step 1: Calculate F_parallel and F_perpendicular:
F_parallel = 1600N * sin(20°) ≈ 547.72N
F_perpendicular = 1600N * cos(20°) ≈ 1484.81N

Step 2: Calculate F_gravity:
F_gravity = 200kg * 9.8m/s^2 = 1960N

Step 3: Determine the net force (F_net):
F_net = F_parallel - F_friction

Step 4: Apply Newton's second law of motion:
F_net = m * a
F_parallel - F_friction = m * a

Step 5: Solve for F_friction:
F_friction = F_parallel - m * a

Step 6: Calculate the coefficient of friction:
coefficient of friction = F_friction / F_perpendicular

Now you can substitute the values into the equations to find the coefficient of friction.