A man is dragging a trunk up the loading ramp of mover's truck. The ramp has a slope angle of 20 degree, and the man pulls upward with a force F whose direction makes an angle of 30 degree with ramp. a) How large a force F is a necessary or the component F, parallel to the ramp to be 60N? b) How large will the component F, then be?

Verified Answer :

Answer:

a.69.3 N

b.34.7 N

Step-by-step explanation:

We are given that

Angle of inclination of the ramp=\(20^{\circ}\)

Force F makes an angle with ramp=\(30^{\circ}\)

The component  of F parallel to the ramp =\(60 N\)

a.We have to find the value of when its horizontal component is 60 N.

We know that

\(F_x=F cos 30^{\circ}\)

\(F=\frac{F_x}{cos 30^{\circ}}\)

\(F=\frac{60}{\frac{\sqrt3}{2}}\)

\(F=40\sqrt3=69.3N\)

b.We have to find \(F_y\) perpendicular to the ramp.

\(F_y=Fsin 30^{\circ}\)

\(F_y=69.3\times \frac{1}{2}=34.7 N\)