A man is dragging a trunk up the loading ramp of a mover’s truck. The ramp has a slope angle of 20.0°, and the man pulls upward
with a force FS whose direction makes an angle of 30.0° with the ramp (Fig. E4.4). (a) How large a force FS is necessary for the component Fx parallel to the ramp to be 90.0 N?(b) How large will the component Fy perpendicular to the ramp be then?
1 answer:
Response:
(a) 104 N
(b) 52 N
Clarification:
Provided Information
Incline angle of the ramp: 20°
F forms a 30° angle with the ramp
The parallel component of F along the ramp is Fx = 90 N.
The perpendicular component of F is Fy.
(a)
Consider the +x direction pointing up the slope, and the +y direction perpendicular to the ramp's surface.
Using the Pythagorean theorem, decompose F into its x-component:
Fx=Fcos30°
To find F:
F= Fx/cos30°
Insert the value for Fx based on the given info:
Fx=90 N/cos30°
=104 N
(b) Calculate the y-component of r using the Pythagorean theorem:
Fy = Fsin 30°
Substituting for F from part (a):
Fy = (104 N) (sin 30°)
= 52 N
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