Question

Two forces act on a 55-kg object. One force has magnitude 65 N directed 59° clockwise from the positive x-axis, and the other has a magnitude 35 N at 32° clockwise from the positive y-axis. What is the magnitude of this objectʹs acceleration? A) 1.1 m/s2 B) 1.3 m/s2 C) 1.5 m/s2

Answer 1

Answer:

A) 1.1 m/s/s

Explanation:

There exist two forces on the object such that

$F_1$ = 65 N directed 59° clockwise from the positive x-axis

$F_2$ = 35 N at 32° clockwise from the positive y-axis

now we have

$F_1 = 65 cos59\hat i - 65 sin59 \hat j$

$F_2 = 35 sin32\hat i + 35 cos32 \hat j$

now the net force on the object is given as

$F_{net} = F_1 + F_2$

$F_{net} = (65 cos59 + 35 sin32)\hat i + (35cos32 - 65 sin59)\hat j$

$F_{net} = 52\hat i - 26 \hat j$

so it's magnitude is given as

$F_{net} = \sqrt{52^2 + 26^2} = 58.15 N$

now from Newton's II law we have

F = ma

$a = \frac{58.15}{55} = 1.1 m/s^2$