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 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

To find the acceleration of the object, we need to first find the net force acting on the object, and then use Newton's second law (F = ma) to find the acceleration.

To find the net force, we can break the given forces into their x and y components:

- The force of magnitude 65 N at 59° clockwise from the positive x-axis has an x component of cos(59°) * 65 N = 32.5 N and a y component of sin(59°) * 65 N = 54.4 N.
- The force of magnitude 35 N at 32° clockwise from the positive y-axis has a y component of cos(32°) * 35 N = 29.2 N and an x component of sin(32°) * 35 N = 18.7 N (since it's directed clockwise from the positive y-axis).

Now, we can add the x and y components separately to get the net force:

- The net x component is 32.5 N + 18.7 N = 51.2 N (to the right)
- The net y component is 54.4 N - 29.2 N = 25.2 N (upwards)

We can use the Pythagorean theorem to find the magnitude of the net force:

net force = sqrt((51.2 N)^2 + (25.2 N)^2) = 57.3 N

Now, we can use Newton's second law to find the acceleration:

F = ma
a = F/m
a = 57.3 N / 55 kg
a = 1.1 m/s^2

Therefore, the magnitude of the object's acceleration is 1.1 m/s^2, which is given by choice A.

Two Forces Act on a 55-Kg Object