Question

Three ants 1,2 & 3 are pulling a grain with forces of magnitude 10N,4N and vector F N as shown in the figure.Find the force vector F if the grain remains in equilibrium under the action of the above forces.
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Answer 1

Given:

Magnitude of force of ant 1 = 10N

Magnitude of force of ant 2 = 4N

To find:

Force vector F.

Solution:

Let  ant 3 make an angle α with -ve y direction.

Equation for summation of forces in x direction =0

10 cos37° - 4 = F sin α

10 * 4/5 - 4 = F sin α

8 - 4 = F sinα

F sin α = 4

Equation of summation forces in the y direction = 0

10 sin37° = F cos α

F cos α = 10 * 3/5

F cosα = 6

|F| = ((F sinα)² + (F cosα)²)^(1/2)

|F| = (4² + 6²)^1/2

|F| = √52

|F| = 2√13

tan α = sinα/ cosα

tanα = 4/6

α = tan(-1) (2/3)

Combining the magnitude and angle of F, we get the vector F.

Therefore, the force vector F is - 2√13 sin 2/√13 i - 2√13 cos 3/√13 j.

Answer 2

Answer:-(4i+6j)N

Explanation: