Two forces P and Q act on an object of mass 9.00 kg with Q being the larger of the two forces. When both forces are directed to the left, the magnitude of the acceleration of the object is 1.20 m/s2. However, when the force P is directed to the left and the force Q is directed to the right, the object has an acceleration of 0.600 m/s2 to the right. Find the magnitudes of the two forces P and Q in newtons.

P = 2.7 N

Q = 8.1 N

Explanation:

Q > P

Both the forces are acting towards the left

Net force = Q + P

Applying newton's 2nd law

net force = mass x acceleration

Q + P = 9 x 1.2 = 10.8 ( 1 )

In the second case Q is acting towards the left and P acts towards the right

so they act in opposite direction

Hence net force = Q - P

Applying newton's 2nd law

net force = mass x acceleration

Q - P = 9 x .6  = 5.4   ( 2 )

Adding ( 1 ) and ( 2 )

2 Q = 16.2

Q = 8.1 N

From ( 1 )

8.1 + P = 10.8 N .

P = 2.7 N