A worker pushes a 1500 N crate with a horizontal force of 345 N a distance of 24 m. Assume the coefficient of kinetic friction between the crate and the floor is .220. How much work is done by the floor on the crate?

-M*g*(mu,k)*X
Mg = 1500 N
mu,k = 0.220
X = 24 m
It is negative because the block's motion is in the opposite direction to the friction force exerted by the floor.

8280J

To calculate the work done by the floor on the crate, we can use the equation:

Work = Force x Distance x cos(theta)

where theta is the angle between the force and the direction of displacement. In this case, since the force and the displacement are in the same direction, cos(theta) = 1.

The force exerted by the floor is equal to the horizontal force applied by the worker minus the force of kinetic friction. So, we can calculate the force exerted by the floor as:

Force(floor) = Force(worker) - Force(friction)

Force(friction) = mu,k * Mg

Plugging in the given values:

Force(worker) = 345 N
Mg = 1500 N
mu,k = 0.220

Force(friction) = 0.220 * 1500 N = 330 N

Force(floor) = Force(worker) - Force(friction) = 345 N - 330 N = 15 N

Now we can calculate the work done by the floor:

Work = Force(floor) x Distance

Work = 15 N x 24 m = 360 Nm

Therefore, the work done by the floor on the crate is 360 Nm.

To calculate the work done by the floor on the crate, we can use the equation:

Work = Force x Distance x cos(theta)

Where:
- Force is the horizontal force exerted by the worker, which is 345 N.
- Distance is the distance over which the crate is pushed, which is 24 m.
- Theta is the angle between the force and the direction of motion. In this case, since the worker pushes horizontally, theta is 0 degrees, and the cosine of 0 degrees is 1.

Therefore, the equation simplifies to:

Work = 345 N x 24 m x cos(0)

However, there's another force acting on the crate which is the friction force between the crate and the floor. The coefficient of kinetic friction between the crate and the floor is given as 0.220.

The frictional force can be calculated as:

Friction Force = coefficient of friction x Normal Force

The normal force is the force perpendicular to the floor, which is equal to the weight of the crate. The weight of the crate is equal to its mass multiplied by the acceleration due to gravity.

Given that the weight of the crate is 1500 N, we can calculate the normal force as follows:

Normal Force = Weight of the crate = 1500 N

Now, substituting the value of the normal force into the equation for friction force:

Friction Force = 0.220 x 1500 N

Finally, to calculate the work done by the floor on the crate, we need to account for the negative direction of the crate's motion, which is opposite to the direction of the friction force. Therefore, the work done by the floor will be the negative value of the work done by the friction force:

Work = - (Friction Force x Distance x cos(theta))

Now you can substitute the values into the equation to find the work done by the floor on the crate.