Question

Two forces P and Q act on an object of mass 11.0 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 0.900 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 0.400 m/s2 to the right. Find the magnitudes of the two forces P and Q .

Answer 1

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 =
`0.900 m/s^(2)`

Acceleration when the forces are in opposite direction, a' =
`0.400 m/s^(2)`

Now,

The net force on the object in first case is given by:

`F_(net) = |\vec{F_(P)}| + |\vec{F_(Q)}| = Ma` (1)

The net force on the object in second case is given by:

`F_(net) = |\vec{F_(P)}| - |\vec{F_(Q)}| = Ma'` (2)

Adding both eqn (1) and (2):

`2|\vec{F_(Q)}| = M(a + a')`

`|\vec{F_(Q)}| = (11.0(0.900 + 0.400))/(2) = 7.15 N`

Putting the above value in eqn (1):

`|\vec{F_(P)}| = 11* 0.900 - |\vec{F_(Q)}|`

`|\vec{F_(P)}| = 9.900 - 7.15 = 2.75`