Two forces, one with a magnitude of 16 N and the other with a magnitude of 29 N are the only forces acting on a 8.5 kg object.What is the maximum...

When two forces act on an object simultaneously:

The magnitude of resultant force is maximum when the two force act in the same direction. The magnitude of this resultant force is equal to the sum of magnitude these two forces.

And the magnitude of resultant force is minimum when the two force act in the opposite direction. The magnitude of this resultant force is equal to the difference in magnitude of these two forces.

Given:

Magnitude of two forces acting on the object are:

f1 = 16 N and f2 = 29 N

Mass of the object = m =8.5 kg

Maximum resultant force acting on object = F(max) = f1 + f2 = 16 + 29 = 45 N

Minimum resultant force acting on object = F(min) = f2 - f1 = 16 - 29 = - 13 N

Maximum acceleration = F(max)/m = 45/8.5 = 5.2941 m/s^2

Maximum accleration = F(max)/m = -13/8.5 = -1.5294 m/s^2

Calculating angle (A) between forces when the acceleration is 3.6 m/s^2

when the acceleration = a = 3.6 m/s^2

resultant force = f = a*m = 3.6*8.5 = 30.6

But: f = (f1^2 + f2^2 + 2f1*f2*Cos A)^1/2

Therefore: 30.6 = (16^2 + 29^2 + 2*16*29*Cos A)^1/2

Therefore: (30.6)^2 = (256 + 841 + 928*Cos A)

Therefore: 936 = (1097 + 928*Cos A)

Therefore Cos A = (936 - 1097)/928 = -0.17349

Therefore A = 170 degrees

Answer:

Magnitude of maximum possible acceleration = 5.2941 m/s^2

Magnitude of minimum possible acceleration = 1.5294 m/s^2 (in opposite direction)

Angle between forces when acceleration is 3.3 m/s^2 = 170 degrees.