The following four forces act on a 4.00 kg object: ₁ = 300 N east ₂ = 700 N north ₃ = 500 N west ₄ = 600 N south What is the acceleration of the object?

Question

Quizplus · Accepted Answer

1. Find the net force in the x-direction:

F_net,x = 300 N east - 500 N west = -200 N

2. Find the net force in the y-direction:

F_net,y = 700 N north - 600 N south = 100 N north

3. Use the net forces to find the acceleration:

F_net = m*a

F_net,x = m*a_x

-200 N = (4.00 kg) * a_x

a_x = -50.0 m/s^2

F_net,y = m*a_y

100 N = (4.00 kg) * a_y

a_y = 25.0 m/s^2

4. Find the magnitude and direction of the acceleration:

a = sqrt(a_x^2 + a_y^2)

a = sqrt((-50.0 m/s^2)^2 + (25.0 m/s^2)^2)

a = 55.9 m/s^2

theta = arctan(a_y / abs(a_x))

theta = arctan(25.0 m/s^2 / 50.0 m/s^2)

theta = 26.6° north of west

Therefore, the best choice is D: 224 N in a direction 26.6° north of west.

The Following Four Forces Act on a 4