Answer:
The magnitude of force on P is 2.75 N
The magnitude of force on Q is 7.15 N
Solution:
As per the question:
Mass of the object, M = 11.0 kg
Acceleration of the object when the forces are directed leftwards, a = [tex]0.900 m/s^{2}[/tex]
Acceleration when the forces are in opposite direction, a' = [tex]0.400 m/s^{2}[/tex]
Now,
The net force on the object in first case is given by:
[tex]F_{net} = |\vec{F_{P}}| + |\vec{F_{Q}}| = Ma[/tex] (1)
The net force on the object in second case is given by:
[tex]F_{net} = |\vec{F_{P}}| - |\vec{F_{Q}}| = Ma'[/tex] (2)
Adding both eqn (1) and (2):
[tex]2|\vec{F_{Q}}| = M(a + a')[/tex]
[tex]|\vec{F_{Q}}| = \frac{11.0(0.900 + 0.400)}{2} = 7.15 N[/tex]
Putting the above value in eqn (1):
[tex]|\vec{F_{P}}| = 11\times 0.900 - |\vec{F_{Q}}|[/tex]
[tex]|\vec{F_{P}}| = 9.900 - 7.15 = 2.75[/tex]
