find the resultant of two forces a b at magnitude10n and 15n respectively acting at a point o at angle of55 also deduce the angle that the resultant forces makes with the components
To find the resultant of the two forces, we can use the parallelogram law of vector addition. Draw a parallelogram with sides representing the two forces, and the diagonal of the parallelogram represents the resultant force.
First, resolve the forces into their components. The component of force A acting along the x-axis is 10*cos(55°) = 5.66N, and the component along the y-axis is 10*sin(55°) = 8.09N. Similarly, the component of force B along the x-axis is 15*cos(55°) = 8.48N, and the component along the y-axis is 15*sin(55°) = 12.14N.
Now, add the components along each axis separately to get the components of the resultant force. The x-component of the resultant = 5.66N + 8.48N = 14.14N. The y-component of the resultant = 8.09N + 12.14N = 20.23N.
The magnitude of the resultant force = sqrt((14.14N)^2 + (20.23N)^2) = 24.29N.
To find the angle that the resultant force makes with the components, we can use the tangent function.
tan θ = (20.23N)/(14.14N) = 1.43
θ = tan^-1(1.43) = 54.2°
Therefore, the angle that the resultant force makes with the components is 54.2°.
To find the resultant of two forces A and B at magnitudes 10 N and 15 N respectively, acting at a point O at an angle of 55 degrees, we can use the method of vector addition.
Let's denote the magnitude and direction of the resultant force as R and θ, respectively.
Step 1: Resolve the forces A and B into their horizontal and vertical components.
Force A:
Magnitude: 10 N
Horizontal component: A_x = A * cos(55°)
Vertical component: A_y = A * sin(55°)
Force B:
Magnitude: 15 N
Horizontal component: B_x = B * cos(0°) (since B is already in the horizontal direction)
Vertical component: B_y = B * sin(0°) (since B is already in the horizontal direction)
Step 2: Calculate the horizontal and vertical components of the resultant force.
Horizontal component of the resultant, R_x = A_x + B_x
Vertical component of the resultant, R_y = A_y + B_y
Step 3: Calculate the magnitude and direction of the resultant force.
Magnitude of the resultant, R = √(R_x^2 + R_y^2)
Direction of the resultant, θ = arctan(R_y / R_x)
Step 4: Substitute the values into the above equations and solve.
Horizontal component of force A:
A_x = 10 N * cos(55°) = 10 N * 0.5736 = 5.736 N
Vertical component of force A:
A_y = 10 N * sin(55°) = 10 N * 0.8192 = 8.192 N
Horizontal component of force B:
B_x =15 N * cos(0°) = 15 N * 1 = 15 N
Vertical component of force B:
B_y = 15 N * sin(0°) = 15 N * 0 = 0 N
Horizontal component of the resultant:
R_x = A_x + B_x = 5.736 N + 15 N = 20.736 N
Vertical component of the resultant:
R_y = A_y + B_y = 8.192 N + 0 N = 8.192 N
Magnitude of the resultant:
R = √(R_x^2 + R_y^2) = √((20.736 N)^2 + (8.192 N)^2) = √(429.98 N^2) = 20.74 N
Direction of the resultant:
θ = arctan(R_y / R_x) = arctan(8.192 N / 20.736 N) ≈ 21.801°
Therefore, the magnitude of the resultant force is 20.74 N, and it makes an angle of approximately 21.801 degrees with the horizontal component.