The magnitude of the vectors F~ is 21 N, the force on the right is applied at an angle 61◦ and the the mass of the block is 54 kg.

Question

The magnitude of the vectors F~ is 21 N, the force on the right is applied at an angle 61◦ and the the mass of the block is 54 kg. If the surface is frictionless, what is the magnitude of the resulting acceleration? Answer in units of m/s 2 .

Here is the image of the problem if you want - https://imgur.com/a/NGVyZKJ

Answer 1

Since the vertical force due to F (on the right) is balanced by the weight and normal force, the acceleration is determined by the horizontal component of each force. Given m =54 kg

Total force in the x direction = 21 + 21 cos 61° = 54a. (no friction, both have the same sense in the x direction)

All you need to do is simplify the left hand side and solve for a.