Harper applies a force of 92 N on a heavy box by using a rope held at an angle of 45 degrees with the horizontal. What are the vertical and horizontal components of the 92N force?
F(hor) =Fcos45
F(vert) =Fsin45
To determine the vertical and horizontal components of a force applied at an angle, you can use trigonometry. In this case, since the angle provided is with respect to the horizontal, we can use the sine and cosine functions.
The vertical component of the force can be calculated using the formula:
Vertical component = Force x sin(angle)
Substitute the values we have:
Vertical component = 92 N x sin(45°)
Using a calculator:
Vertical component ≈ 92 N x 0.7071
Vertical component ≈ 65.69 N
Therefore, the vertical component of the 92 N force is approximately 65.69 N.
The horizontal component of the force can be calculated using the formula:
Horizontal component = Force x cos(angle)
Substitute the values we have:
Horizontal component = 92 N x cos(45°)
Using a calculator:
Horizontal component ≈ 92 N x 0.7071
Horizontal component ≈ 65.69 N
Therefore, the horizontal component of the 92 N force is approximately 65.69 N.