Question

Forces is F1(east) and F2 are simultaneously applied to
a 30kg mass. When f2is east , a = 5.0 m/s2 east and
When F2 is west a=10m/s² east - Determine the
Magnitude of f1 and f2

Answer 1

There's a problem with the given information, but I'll get to that later.

Use Newton's second law. When F₂ points east, we have

F₁ + F₂ = (30 kg) (5.0 m/s²) = 150 N

and when F₂ points west, it acts in the opposite direction and

F₁ - F₂ = (30 kg) (10 m/s²) = 300 N

Solve for F₁ and F₂ : we have

(F₁ + F₂) + (F₁ - F₂) = 150 N + 300 N

2F₁ = 450 N

F₁ = 225 N

and

(F₁ + F₂) - (F₁ - F₂) = 150 N - 300 N

2F₂ = -150 N

F₂ = -75 N

But F₁ and F₂ are magnitudes, so they must be positive! Also, it doesn't make sense that when the forces both point east, the mass accelerates less than it does when the forces work against each other. Probably one of the given accelerations are supposed to point west instead of east.