Final answer:
The magnitude of the horizontal force (fgx) acting on a 10 kg block on a ramp inclined at 45 degrees is approximately 69.29 N. It is found by multiplying the total gravitational force by the cosine of the angle of the incline.
Step-by-step explanation:
To find the magnitude of the horizontal force (fgx) acting on a 10 kg block resting on a ramp inclined at 45 degrees, we can use the components of the gravitational force. The gravitational force can be broken down into a component parallel to the incline (fgx) and a component perpendicular to the incline (fgy).
The gravitational force acting on the block is equal to the mass of the block (m) times the acceleration due to gravity (g), so Fgravity = m × g. Assuming g is 9.8 m/s2, the gravitational force on the block is 10 kg × 9.8 m/s2 = 98 N.
To find the horizontal component fgx of the gravitational force, we use the cosine of the angle because fgx is adjacent to the angle:
- fgx = Fgravity × cos(45°)
- fgx = 98 N × cos(45°)
- fgx = 98 N × 0.707
- fgx = 69.29 N
Therefore, the magnitude of the horizontal force acting on the block is approximately 69.29 N.