A block is moving down an incline a distance of 5 m form point A to point B by a force F that is parallel to the incline and has magnitude 2 N. The magnitude of the frictional force acting on the block is 10 N. If the kinetic energy of the block increases by 35 J between A and B how much work is done on the block by gravitational force as the block moves from A to B?

Is this the equation I would use: mgh =1/2mv^2?

No, you don't use that equation. You use a conservation of energy equation that includes the frictional work done.

Work done by force F = 10 J
= (kinetic energy increase) + (potential energy increase) + (frictional heating)

In your case, the potential energy decreases. That decrease is the work done BY gravity. The frictional heating is 10 N x 5 m = 50 J

To find the work done by the gravitational force as the block moves from point A to point B, we need to consider the work done by force F (parallel to the incline), the change in kinetic energy, the change in potential energy, and the work done by the frictional force.

Let's break it down step by step:

1. Work done by force F:
Since the applied force F is parallel to the incline, the work done by this force can be calculated using the equation:

Work = Force x Distance x cos(angle) (where angle is the angle between the force and the displacement)

In this case, the magnitude of the force F is 2 N and the distance traveled is 5 m. Since the force is parallel to the incline, the angle between the force and the displacement is 0 degrees. Therefore, the work done by force F is:

Work = 2 N x 5 m x cos(0 degrees) = 10 J

2. Change in kinetic energy:
The change in kinetic energy can be calculated using the equation:

Change in Kinetic Energy = Final Kinetic Energy - Initial Kinetic Energy

Since the problem states that the kinetic energy of the block increases by 35 J between points A and B, the change in kinetic energy is:

Change in Kinetic Energy = 35 J

3. Change in potential energy:
The change in potential energy can be calculated using the equation:

Change in Potential Energy = Final Potential Energy - Initial Potential Energy

Since the block moves from a higher point (point A) to a lower point (point B) on the incline, the change in potential energy is negative. In this case, we can equate the change in potential energy to the work done by gravity:

Change in Potential Energy = - Work done by gravity

4. Work done by the frictional force:
The work done by the frictional force can be calculated using the equation:

Work = Force of friction x Distance

In this case, the magnitude of the frictional force is 10 N and the distance traveled is 5 m. Therefore, the work done by the frictional force is:

Work = 10 N x 5 m = 50 J

Putting it all together:

Work = (Change in Kinetic Energy) + (Change in Potential Energy) + (Work done by friction)

Since we are looking for the work done by gravity, we can express it as:

Work done by gravity = (Change in Kinetic Energy) + (Change in Potential Energy) + (Work done by friction)

Substituting the known values:

Work done by gravity = 35 J + (Change in Potential Energy) + 50 J

Simplifying the equation and rearranging:

Change in Potential Energy = Work done by gravity - (Change in Kinetic Energy) - (Work done by friction)

By substituting the values, you can find the exact amount of work done by the gravitational force as the block moves from point A to point B using this equation.