A 1.20*10^2 kg crate is being pushed across a horizontal floor by a force P that makes an angle of 30.0° below the horizontal. The coefficient of kinetic friction is 0.350. What should be the magnitude of P, so that the net work done by it and the kinetic frictional force is zero?

So P is pointing UP?

If so, a portion of P counters weight, and in so doing, reduces friction to zero.

Psin30=mg
P= 2mg

If the net force is zero, the friction force balances the horizontal component of the applied force P.

Calculate the Friction force and divide it by cos 30.

The fact that the applied force is 30 deg below horizontal will affect the friction force.

My interpretation of the problem is different from Bob's. I did not assume that the friction was reduced to zero, only that it balances the applied force to make the net force (and work) zero.

To find the magnitude of force P that will result in zero net work, we need to equate the work done by force P to the work done by the kinetic frictional force.

The work done by a force is given by the formula:

Work = force * displacement * cos(angle)

Let's break down the problem step by step:

Step 1: Determine the force of kinetic friction.
The force of kinetic friction can be calculated using the formula:

Force of kinetic friction = coefficient of kinetic friction * normal force

In this case, the normal force is equal to the weight of the crate, which can be calculated as:

Weight = mass * acceleration due to gravity

Step 2: Calculate the displacement of the crate.
Since the crate is being pushed horizontally, the displacement will be the distance covered by the crate.

Step 3: Determine the work done by force P.
To find the work done by force P, we need to calculate the magnitude of the horizontal component of P. This can be found using trigonometry:

Horizontal component of P = P * cos(angle)

Now, we can calculate the work done by force P using the work formula:

Work by force P = force P * displacement * cos(0°)

Step 4: Equate the work done by force P to the work done by the kinetic frictional force.
Since we want the net work to be zero, we set the equation:

Work by force P = Work by kinetic friction

(force P * displacement * cos(0°)) = (force of kinetic friction * displacement)

Finally, we can solve for force P by rearranging the equation:

force P = (force of kinetic friction) / cos(0°)

Remember that the magnitude of the force P should be equal to or greater than the resultant force of the kinetic friction, otherwise the net work will not be zero.