Question

A 30 kg block on a frictionless surface experiences two perpendicular forces in the x and y directions. If the force in the x direction is 60 N, and the force in the y direction is 150 N, find the acceleration in the x-direction, the y-direction, and the net resultant acceleration.

Answer 1

Question#18771

A 30 kg block on a frictionless surface experiences two perpendicular forces in the x and y directions. If the force in the x direction is 60 N, and the force in the y direction is 150 N, find the acceleration in the x-direction, the y-direction, and the net resultant acceleration.

Solution:

Such as the force's directions are perpendicular the accelerations are:

$$a _ {x} = \frac {F _ {x}}{m} = \frac {6 0}{3 0} = 2 \, \mathrm{m/s^2}$$ $$a _ {y} = \frac {F _ {y}}{m} = \frac {1 5 0}{3 0} = 5 \, \mathrm{m/s^2}$$

The resultant acceleration is:

$$a _ {R} = \sqrt {a _ {x} ^ {2} + a _ {y} ^ {2}} = \sqrt {2 ^ {2} + 5 ^ {2}} = 5.39 \, \mathrm{m/s^2}$$