A block of mass m = 14 kg is pressed with a horizontal force F against a frictionless ramp of angle θ = 78∘.

What is the magnitude of the normal force exerted by the incline surface on the block?

The angle is measured how?

with respect to horizontal

To find the magnitude of the normal force exerted by the incline surface on the block, we need to analyze the forces acting on the block.

The forces acting on the block are:
1. The weight of the block (mg), acting vertically downward.
2. The normal force (N), perpendicular to the incline surface.
3. The force applied horizontally (F), directed up the incline.

Since the ramp is frictionless, there is no friction force to consider.

Next, we can resolve the forces into components parallel and perpendicular to the incline.

1. Weight (mg):
The weight of the block can be resolved into two components:
- The component parallel to the incline is mg*sin(θ).
- The component perpendicular to the incline is mg*cos(θ).

2. Force applied horizontally (F):
The force applied can be resolved into two components:
- The component parallel to the incline is F*cos(θ).
- The component perpendicular to the incline is F*sin(θ).

Using Newton's second law, we can write the equation of motion along the incline direction:
F_parallel = m*a
(F*cos(θ)) - (mg*sin(θ)) = m*a

Since the block is not accelerating in the vertical direction, the sum of the forces perpendicular to the incline must be zero:
N - (mg*cos(θ)) - (F*sin(θ)) = 0

We can rearrange the equation to solve for N:
N = mg*cos(θ) + F*sin(θ)

Plugging in the given values:
m = 14 kg
θ = 78°
F = (Given force)

We can calculate the magnitude of the normal force exerted by the incline surface on the block using the equation N = mg*cos(θ) + F*sin(θ).