The following forces act on a body:F1=5,3Nupwards.F2=2,2N upwards and F3=10,7 N downwards.Determine the resultant of the three forces using a sketch of head to tail vector diagram and check your answer with equation :FR=F1+F2+F3

Fr = 5.3 + 2.2 - 10.7 = -3.2 N. =

3.2 N. downward.

Sketch: From a point, draw 2 arrows pointing upward and one arrow pointing downward.

To find the resultant of the three forces, F1, F2, and F3, we can start by drawing a sketch of the head-to-tail vector diagram. The magnitudes and directions of the forces are as follows:

F1 = 5.3 N upwards
F2 = 2.2 N upwards
F3 = 10.7 N downwards

Step 1: Start by drawing a line segment to represent the first force, F1. Since F1 is 5.3 N and upwards, draw the line segment upwards with a length proportional to 5.3 units.

Step 2: Next, draw the second force, F2. Since F2 is 2.2 N and upwards, draw another line segment upwards with a length proportional to 2.2 units. This line should start from the endpoint of the previous line segment.

Step 3: Finally, draw the third force, F3. Since F3 is 10.7 N and downwards, draw another line segment downwards with a length proportional to 10.7 units. This line should start from the endpoint of the previous line segment.

Step 4: Complete the vector diagram by drawing a straight line connecting the starting point of the first force to the ending point of the last force. This line represents the resultant force, FR.

Step 5: To determine the magnitude and direction of FR, measure the length of the resulting line segment on the diagram and also the angle it makes with a reference direction (such as the positive x-axis).

Now let's calculate FR using the given equation: FR = F1 + F2 + F3

FR = (5.3 N upwards) + (2.2 N upwards) + (10.7 N downwards)

Since the forces are in opposite directions, we need to subtract the magnitude of F3 from the combined magnitudes of F1 and F2:

FR = (5.3 N + 2.2 N) - 10.7 N

FR = 7.5 N - 10.7 N

FR = -3.2 N

The magnitude of the resultant force is 3.2 N and its direction is downwards, opposite to the direction of F3.

Please note that the negative sign indicates the opposite direction of F3.

To determine the resultant of the three forces F1, F2, and F3 using a sketch of a head to tail vector diagram, follow these steps:

1. Draw a point representing the starting position of the vector diagram.
2. From this point, draw a ray upwards representing the direction and magnitude of the first force F1 = 5.3 N. Label the arrowhead as F1.
3. From the end of the F1 arrow, draw a second ray upwards representing the direction and magnitude of the second force F2 = 2.2 N. Label the arrowhead as F2.
4. From the end of the F2 arrow, draw a third ray downwards representing the direction and magnitude of the third force F3 = 10.7 N. Label the arrowhead as F3.
5. Connect the starting point of the vector diagram to the end of the F3 arrow to form a closed triangle.
6. The resultant of the three forces, FR, is the diagonal line drawn from the starting point to the opposite vertex of the triangle.
7. Measure the length and direction of the resultant line using a ruler and protractor.

To check the answer using the equation FR = F1 + F2 + F3, follow these steps:

1. Determine the x and y components of each force. The x component is the force multiplied by the cosine of the angle with the x-axis, and the y component is the force multiplied by the sine of the angle.
- F1x = F1 * cos(theta1)
- F1y = F1 * sin(theta1)
- F2x = F2 * cos(theta2)
- F2y = F2 * sin(theta2)
- F3x = F3 * cos(theta3)
- F3y = F3 * sin(theta3)
(Assuming theta1, theta2, and theta3 are the angles each force makes with the positive x-axis.)

2. Sum up the x and y components of the forces.
- Sum of x components = F1x + F2x + F3x
- Sum of y components = F1y + F2y + F3y

3. Calculate the magnitude and direction of the resultant using the Pythagorean theorem and trigonometry.
- Magnitude of FR = sqrt((Sum of x components)^2 + (Sum of y components)^2)
- Direction of FR = arctan((Sum of y components) / (Sum of x components))

4. Compare the magnitude and direction obtained from the equation with those measured from the vector diagram. They should be consistent if calculated correctly.

By following these steps, you can determine the resultant of the three forces and check the answer using the equation FR = F1 + F2 + F3.