Find the resultant force.

Question

 Given the following F = 3 i – 7.5 j and a force vector B that has a magnitude of 8 N and makes an

angle counterclockwise from the x axis at 23 degrees. Find the resultant force. And the

acceleration vector if that resultant force is applied to an object with a mass of 0.53 Kg

Answer 1

The first force F = (3, -7.5) is already in component form.

To write the force B in component form, simply compute the following:

B = (|B|cosθ, |B|sinθ) = (8cos(23 deg), 8sin(23 deg)) ≈ (7.364, 3.126).

To find the resultant force, add the forces F and B component-wise:

F_resultant = F + B = (3 + 8cos(23 deg), -7.5 + 8sin(23 deg)) ≈ (3 + 7.364, -7.5 + 3.126) = (10.364, -4.374).

To find the acceleration vector, recall that a = F/m from newton's second law, so we just need to multiply the resultant force by the multiplicative inverse of the mass:

a_resultant = (1/m)*F_resultant ≈ (1/0.53)*(10.364, -4.374) = (10.364/0.53, -4.374/0.53) = (19.555, -8.253).