Newton's second law: Two forces act on a 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 object's acceleration? A) 1.1 m/s² B) 1.3 m/s² C) 1.5 m/s² D) 1.7 m/s²

Question

Quizplus · Accepted Answer

First, we need to resolve the forces into their x and y components. For the 65 N force, we have:

Fx = 65 cos(59°) = 33.6 N
Fy = -65 sin(59°) = -53.8 N (negative because it's in the negative y direction)

For the 35 N force, we have:

Fx = 35 sin(32°) = 18.1 N
Fy = 35 cos(32°) = 28.2 N

Now we can add up all the forces:

ΣFx = 33.6 N + 18.1 N = 51.7 N
ΣFy = -53.8 N + 28.2 N = -25.6 N

Next, we can use Newton's second law: F = ma. We can apply this equation separately to the x and y directions:

ΣFx = ma
ΣFy = ma

We want to find the magnitude of the acceleration, so we can combine these two equations:

ΣF = sqrt((ΣFx)^2 + (ΣFy)^2) = sqrt((51.7 N)^2 + (-25.6 N)^2) = 57.5 N

Then we solve for a:

a = ΣF/m = 57.5 N / (11eb6b7b_2f24_75de_b0cf_03fed02127c9_TB8274_11 kg) = 1.1 m/s^2

Therefore, the answer is A) 1.1 m/s^2.

Newton's Second Law: Two Forces Act on a Object