The magnitude and direction of the acceleration produced in a body of mass 5 ~kg$5 \mathrm{~kg}$ when two mutually perpendicular forces 8 ~N$8 \mathrm{~N}$ and 6 ~N$6 \mathrm{~N}$ act on it, are respectively:

Related Formula

Core Logic

When the trolley accelerates with a$a$, a pseudo force F = ma$F = ma$ acts on the box in the backward direction relative to the trolley. To prevent the box from slipping, the static friction force must balance this pseudo force. The maximum available static friction is fs,max = μₛ N = μₛ mg$f_{s,\text{max}} = \mu_s N = \mu_s mg$.

Step 1: Calculate Maximum Acceleration

Equating the pseudo force to maximum static friction:

Substitute the given values (μₛ = 0.12, g = 10 ~m/s²$\mu_s = 0.12, g = 10 \mathrm{~m/s}^2$):

Pattern Recognition

The mass of the box is completely irrelevant in this calculation because it cancels out on both sides of the equation. Max non-slip acceleration is always simply μₛ g$\mu_s g$.

Chapter Mix

Class 11 Physics: Laws of Motion