Completed Question:
Your neighbor Paul has rented a truck with a loading ramp. The ramp is tilted upward at 35 ∘,and Paul is pulling a large crate up the ramp with a rope that angles 10 ∘ above the ramp. Paul pulls with a force of 350 N. (Force is measured innewtons, abbreviated N.)
What is the magnitude of the horizontal component of his force?
What is the magnitude of the vertical component of his force?
Answer:
Both are 175√2 N.
Explanation:
The ramp does an angle of 35° if the soil and the rope that he's pulling does an angle of 10° with the ramp. So, the total angle that the rope does with the soil is 45° (10° + 35°).
The force is a vector, it means that it has a module, direction, and sense. So, if the force acts at an angle of 45° with the horizontal (the soil), the vector can be decomposed to vertical and horizontal vectors.
The decomposition helps to study the movement because an inclined force acts both horizontally and vertically. By the sin and cos of a triangle, the horizontal (x) and vertical (y) forces are:
Fx = F*cosα
Fy = F*sinα
Where α is the angle with the horizontal, and sin45° = cos45° = √2/2
Fx = 350*cos45° =350*√2/2
Fx = 175√2 N
Fy = 350*sin45° = 350*√2/2
Fy = 175√2 N
