Question

Two forces act on a moving object that has a mass of 27 kg. One force has a magnitude of 12 N and points due south, while the other force has a magnitude of 17 N and points due west. What is the acceleration of the object

Answer 1

Answer:

mag (a) = 0.7707 m/s^2

a = - 0.62963 i - 0.4444 j

Explanation:

Given:

- Force 1 , F_1 = - 12 j

- Force 2, F_2 = - 17 i

- mass of the object m = 27 kg

Find:

What is the acceleration of the object

Solution:

- The relation between the Force vector and the acceleration vector of an object can be given by the Newton's Second Law of motion:

                                   F = m*a

Where a is the acceleration vector.

                                  (-17 i - 12 j ) = m*a

                                  a = (-17 i - 12 j ) / 27

                                 a = - 0.62963 i - 0.4444 j

- The magnitude of the acceleration mag (a) is given by:

                                 mag (a) = sqrt ( (-0.62963)^ 2 + (-0.44444)^2 )

                                 mag (a) = sqrt ( 433/729)

                                mag (a) = 0.7707 m/s^2

Answer 2

Answer:

The acceleration of the object is  0.77$m/s^{2}$ in the negative x and y direction.

Explanation:

Given;

$F_{1}$ = 12N (due South)

$F_{2}$ = 17N (due West)

The resultant force F acting on the body is given by;

F = $\sqrt{F_{1} ^{2} + F_{2} ^{2}}$

F = $\sqrt{12^{2} + 17^{2}}$

F = $\sqrt{144 + 289}$

F = $\sqrt{433}$

F = 20.8N

This resultant force will act on the body and cause the acceleration.

Using Newton's law of motion;

F = m x a

Where;

F = resultant force = 20.8N

m = mass of the object = 27kg

=> 20.8 = 27 x a

=> a  = 20.8 / 27

=> a = 0.77$m/s^{2}$

And since the forces are acting due South and due West, the direction of acceleration will be in the negative -x and -y direction.