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? (a) 0.63m/s2 directed 55∘ south of west (b) 0.44m/s2 directed 24∘ south of west (c) 0.77m/s2 directed 35∘ south of west (d) 0.77m/s2 directed 55∘ south of west (e) 1.1m/s2 directed 35∘ south of west

Answer 1

Answer:

(c) 0.77 m/s^2 directed 35° south of west.

Explanation:

Let's first find the resultant force and its direction:

$F = \sqrt{(F_S)^2 + (F_W)^2}$

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

F = 20.808 N

To find the direction, we can just imagine the forces as lengths of a right angled triangle.

So, Force (west) will be our perpendicular.

and Force (south) will be our base.

Calculating the angle we have:

$Tan(Theta) = \frac{17}{12}$

Theta = 54.78°    (angle from south)

Direction of resultant force = 90 - 54.78 = 35.22° (south of west)

Taking out the acceleration, we get:

F = m * a

20.808 = 27 * a

a = 0.77 m/s^2

So the answer is (c)

Answer 2

The required magnitude of acceleration is $0.77 \;\rm m/s^{2}$ at 55 degrees from south of west. Hence, option (c) is correct.

Given data:

The mass of object is, m = 27 kg.

The magnitude of force towards the south is, F = 12 N.

The magnitude of force towards the west is, F' = 17 N.

Here we will follow the Newton's second law that applied force will cause to accelerate the object along the same direction.

Then net force is,

$F_{net}= \sqrt{F^{2}+F'^{2}}\\\\F_{net}= \sqrt{12^{2}+17^{2}}\\\\F_{net} = 20.808 \;\rm N$

Now, the direction will be,

$tan \theta =\dfrac{F'}{F} \\\\tan \theta =\dfrac{17}{12} \\\\\theta \approx 55^{\circ}$

This is the direction of 55 degrees towards south. So, acceleration will be towards south of west.

Then,

$F_{net} = m a\\\\20.808 = 27 \times a\\\\a = 0.77 \;\rm m/s^{2}$

Thus, we can conclude that the required magnitude of acceleration is $0.77 \;\rm m/s^{2}$ at 55 degrees from south of west. Hence, option (c) is correct.

Learn more about the Newton's second law here:

https://brainly.com/question/19860811