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Chapter 1: Q4E (page 124)

A man is dragging a trunk up the loading ramp of a mover鈥檚 truck. The ramp has a slope angle of 20掳, and the man pulls upward with a force F鈫�whose direction makes an angle of 30掳with the ramp (Fig. E4.4).

(a) How large a force F鈫�is necessary for the component Fxparallel to the ramp to be 90.0 N?

(b) How large will the component Fy perpendicular to the ramp be then?

Short Answer

Expert verified

(a)The magnitude of the forceF鈫� has to be 103.9N for the component Fxparallel to the ramp to be 90.0 N.

(b) The component Fyperpendicular to the ramp will be 51.95N

Step by step solution

01

Given data

The component of the force parallel to the ramp is

Fx=90N

The angle made by the force with the ramp is

胃=30掳

02

Vector components

The X and Y components of a vector A鈫� making an angle 胃 with the X axis can be summarized as

A鈫�=Acos胃i^+Asin胃j^.....1

03

Components of the forces

From equation (1), the x component of the force is

Fx=Fcos胃Fcos30掳=90NF=90cos30掳N=103.9N

From equation (1), the y component of the force is

Fy=Fsin胃=103.9脳sin30掳N=51.95N

The net magnitude of the force is 103.9N and the component perpendicular to the ramp is 51.95N.

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