two force10n and20n are inclined at an angle 60 degree to each.find the resultant forces are now made to be inclined at120degree to each other,find the magnitude of the new resultant force
90
100+400-2*10*20*cos60=100+400-400*1/2=500-200=300=√300=17.32050808
To find the resultant force, we can use the parallelogram law of vector addition.
Step 1: Resolve the forces into their horizontal and vertical components.
The horizontal component of a force F can be calculated using the formula: Fx = F * cos(angle)
The vertical component of a force F can be calculated using the formula: Fy = F * sin(angle)
For the first force of 10N, the horizontal component is: F1x = 10N * cos(60°) = 5N
And the vertical component is: F1y = 10N * sin(60°) = 8.66N (rounded to two decimal places)
For the second force of 20N, the horizontal component is: F2x = 20N * cos(60°) = 10N
And the vertical component is: F2y = 20N * sin(60°) = 17.32N (rounded to two decimal places)
Step 2: Add the horizontal and vertical components separately for the two forces.
Horizontal component of resultant force = F1x + F2x = 5N + 10N = 15N
Vertical component of resultant force = F1y + F2y = 8.66N + 17.32N = 25.98N (rounded to two decimal places)
Step 3: Find the magnitude of the resultant force.
The magnitude of the resultant force can be calculated using the Pythagorean theorem.
Resultant force = sqrt((horizontal component)^2 + (vertical component)^2)
Resultant force = sqrt((15N)^2 + (25.98N)^2) = 30.19N (rounded to two decimal places)
Therefore, the magnitude of the new resultant force is approximately 30.19N.