Final answer:
The work done by force F involves the vertical component of the force because it's the direction of movement. The work done by gravity is negative due to its opposing direction, and the normal force does no work. The increase in gravitational potential energy is calculated with the product of mass, gravity, and height change.
Step-by-step explanation:
To tackle this problem, we need to apply the concepts of work and energy in physics. The problem involves calculating work done by different forces while pushing a block up a vertical wall, taking into account the angle of application of the force, friction, and gravity.
Work Done by Force F
The work done by a force is given by the equation W = Fd cos(θ), where F is the force applied, d is the distance moved by the object, and θ is the angle between the force and the displacement. Since the force F is applied at 30 degrees to the horizontal, we'll also consider the vertical component of this force because that's the direction of the displacement.
Work Done by Gravity
The work done by gravity will be negative since gravity is acting in the opposite direction to the displacement. It can be calculated with W = mgh, where m is mass, g is acceleration due to gravity, and h is the change in height.
Work Done by the Normal Force
The work done by the normal force will be zero since the normal force acts perpendicular to the displacement and thus does not contribute to work in the direction of the block's movement.
Change in Gravitational Potential Energy
The increase in gravitational potential energy is equal to the work done against gravity and can be calculated using ΔPE = mgh.