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

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 = $0.900 m/s^{2}$

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):

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

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

Putting the above value in eqn (1):

$|\vec{F_{P}}| = 11\times 0.900 - |\vec{F_{Q}}|$

$|\vec{F_{P}}| = 9.900 - 7.15 = 2.75$