Question

Two forces, 300 N and 500 N, act on an 80-kg particle. 300 N north and 500 N east. Find the magnitude of the resultant acceleration if the forces make a 90 angle with each other.

Answer 1

7.28 m/s^2.

Step-by-step explanation:

To find the magnitude of the resultant acceleration of the particle, we can use the equation for Newton's second law of motion:

F = ma

Where F is the resultant force, m is the mass of the particle, and a is the resultant acceleration.

Since the forces are acting at a 90 degree angle to each other, we can treat them as two separate forces and use the Pythagorean theorem to find the magnitude of the resultant force:

F = sqrt((300 N)^2 + (500 N)^2)

= sqrt(90000 N^2 + 250000 N^2)

= sqrt(340000 N^2)

= sqrt(340000) N

= 582.67 N

We can now use this value for the resultant force to find the resultant acceleration:

a = F/m

= 582.67 N / 80 kg

= 7.28 m/s^2

Therefore, the magnitude of the resultant acceleration is 7.28 m/s^2.