   Chapter 4, Problem 12P

Chapter
Section
Textbook Problem

Two forces are applied to a car in an effort to move it, as shown in Figure P4.12. (a) What is the resultant vector of these two forces? (b) If the car has a mass of 3 000 kg, what acceleration does it have? Ignore friction. Figure P4.12

(a)

To determine
The resultant vector of the forces.

Explanation

Section 1:

Explanation:

Given info: The magnitude of the two forces are F1 = 400 N and F2 = 450 N. The angle of inclination of F1 and F2 are marked in the figure. The mass of the car is 300 kg.

The forces along the x and y directions are given in the figure below.

The total force along the x-axis is,

Fx=F1sin30°F2sin10°

Substitute 400 N for F1 and 400 N for F2 in the above expression.

Fx=(400N)(0.5)(450N)(0.174)=121.86N

The fifference between the two forces is taken because the directions are opposite.

The total force along the y-axis is,

Fy=F1cos30°+F2cos10°

Substitute 400 N for F1 and 400 N for F2 in the above expression.

Fy=(400N)(0.866)+(450N)(0

(b)

To determine
The acceleration of the car.

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