Solve this question, the resultant of two force acting at right angle to each other on a body is ten newton. If the angle between the resultant and one of the force is sixty degree, find the force.
Three vectors are shown in Fig. 3-32 (A = 68.0 , B = 50.0°). Their magnitudes are given in arbitrary units. Determine the sum of the three vectors.
Figure 3-32
(a) Give the resultant in terms of components.
Rx =
Ry =
(b) What is the magnitude of the resultant?
What is the resultant's angle above the +x axis?
°
Tow forces whose resultant is 100N are at right angle to each other.if one of them makes an angle of 30 with the resultant def.its magnitude
F = 10*Cos60 = 5 N.
Fr = 100N.[30o].
F = 100*Cos30 = 86.6 N.
To solve this problem, we can use the concept of vector addition and trigonometry. Here's how:
Step 1: Draw a diagram
Start by drawing a diagram to visualize the situation. Draw two forces at right angles to each other, and label the resultant force as "10 N." Label the angle between the resultant force and one of the original forces as 60 degrees.
Step 2: Split the resultant force into its components
Since the original forces are at right angles, the resultant force can be divided into two components: one in the direction of the given force and one perpendicular to it. Use trigonometry to split the resultant force into its components.
Let the magnitude of the force acting at the 60-degree angle be 'F'. The component of the resultant force in the direction of this force will be F * cos(60°), and the component perpendicular to this force will be F * sin(60°).
Step 3: Write the equations
The sum of the components in the direction of the force should equal the magnitude of the force itself:
F * cos(60°) = F
The sum of the components perpendicular to the force should equal 10 N (the magnitude of the resultant force):
F * sin(60°) = 10 N
Step 4: Solve the equations
Use the properties of trigonometric functions to solve the equations. In this case, we can use the fact that cos(60°) = 0.5 and sin(60°) = sqrt(3)/2.
From the first equation:
F * 0.5 = F
0.5F = F
0.5 = 1
From the second equation:
F * sqrt(3)/2 = 10
sqrt(3)F = 20
F = 20/sqrt(3)
F ≈ 11.55 N
Therefore, the force acting at a 60-degree angle is approximately 11.55 Newtons.