Three forces act on a moving object. One force has a magnitude of 81.2 N and is directed due north. Another has a magnitude of 47.9 N and is directed due west. What must be (a) the magnitude and (b) the direction of the third force, such that the object continues to move with a constant velocity? Express your answer as a positive angle south of east.

Question

Three forces act on a moving object. One force has a magnitude of 81.2 N and is directed due north. Another has a magnitude of 47.9 N and is directed due west. What must be (a) the magnitude and (b) the direction of the third force, such that the object continues to move with a constant velocity? Express your answer as a positive angle south of east.

Answer 1

X = -47.9 N.

Y = 81.2 N.
Q2.

a. F3 = Sqrt(X^2 + Y^2)

b. Tan A = Y/X = 81.2/-47.9 = -1.69520.
A = -59.5o = 59.5o N. of W.

Direction = 59.5o S. of E.

Answer 2

To find the magnitude and direction of the third force that will allow the object to move with a constant velocity, we need to use vector addition.

Let's start by representing the forces graphically.

Force 1: 81.2 N due north (up)
Force 2: 47.9 N due west (left)

We can draw a vector diagram to find the resultant vector.

Step 1: Draw a vertical line representing the north direction and label it 81.2 N.
Step 2: Draw a horizontal line representing the west direction and label it 47.9 N.
Step 3: Connect the two lines using a vector triangle.

Now, we need to find the magnitude and direction of the third force (resultant) that will complete the triangle and allow the object to move with a constant velocity. To find the magnitude, we can use the Pythagorean theorem:

Resultant's magnitude = sqrt((81.2^2) + (47.9^2))

Calculating this value, the magnitude of the resultant is approximately 94.1 N.

To find the direction, we can use trigonometry.

tan(theta) = (opposite/adjacent) = (81.2/47.9)

Therefore, the angle, theta, is given by:

theta = arctan(81.2/47.9)

Calculating this value, theta is approximately 59.8 degrees.

Now, to express the angle south of east, we need to subtract theta from 180 degrees:

Angle south of east = 180 - 59.8

Angle south of east is approximately 120.2 degrees.

Therefore, the magnitude of the third force is approximately 94.1 N, and its direction is approximately 120.2 degrees south of east.

Answer 3

To find the magnitude and direction of the third force, we need to understand the concept of vector addition.

When multiple forces act on an object, they can be added together as vectors to get the resultant force. The resultant force is the single force that represents the combined effect of all individual forces acting on the object.

In this case, we have two forces: one with a magnitude of 81.2 N in the north direction, and another with a magnitude of 47.9 N in the west direction. Let's represent these forces as vectors:

F1 = 81.2 N (north)
F2 = 47.9 N (west)

To find the magnitude and direction of the third force (F3), we need to add the vectors F1 and F2. We can do this using the Pythagorean theorem for the magnitude and trigonometry for the direction.

First, let's find the magnitude:

Magnitude of F3 = √(Magnitude of F1)^2 + (Magnitude of F2)^2
= √(81.2 N)^2 + (47.9 N)^2
= √(6591.44 N^2 + 2294.41 N^2)
= √(8885.85 N^2)
≈ 94.22 N

The magnitude of the third force (F3) is approximately 94.22 N.

Next, let's find the direction:

Direction of F3 = tan^(-1)((Magnitude of F2)/(Magnitude of F1))
= tan^(-1)((47.9 N)/(81.2 N))

Using a calculator, we find the angle to be approximately 30.86 degrees.

Since the question asks for the angle south of east, we need to subtract this angle from 180 degrees:

Angle south of east = 180 - 30.86
≈ 149.14 degrees

Therefore, the magnitude of the third force is approximately 94.22 N, and the direction is approximately 149.14 degrees south of east.