A 60 kg body is pushed with just enough force to start it moving across a floor and the same force continues to act afterwards. The coefficients of static and sliding friction are 0.5 and 0.4 respectively. The acceleration of the body is

The correct answer is 1 m/sec².

In this problem, a 60 kg body is pushed with just enough force to start moving. This is a key phrase — it means the applied force equals the maximum static friction force. Once the body starts sliding, only kinetic (sliding) friction acts, which is less than static friction. The same applied force now produces a net force and hence an acceleration.

Given Data:

Mass, m = 60 kg
Coefficient of static friction, μ_s = 0.5
Coefficient of sliding (kinetic) friction, μ_k = 0.4
Acceleration due to gravity, g = 9.8 m/s²

Step 1: Find the Applied Force

The applied force is just enough to initiate motion, so it equals the maximum static friction:

F={\mu }_s\times m\times g

F=0.5\times 60\times 9.8

F=294\text{N}

Step 2: Find the Kinetic (Sliding) Friction Force

Once the body is in motion, the friction that opposes it is kinetic friction:

f_k={\mu }_k\times m\times g

f_k=0.4\times 60\times 9.8

f_k=235.2\text{N}

Step 3: Calculate the Net Force

The same applied force of 294 N continues to act. The net force on the body while sliding is:

F_{\mathrm{net}}=F-f_k

F_{\mathrm{net}}=294-235.2=58.8\text{N}

Step 4: Apply Newton's Second Law to Find Acceleration

a=\frac{F_{\mathrm{net}}}{m}=\frac{58.8}{60}

a=0.98\text{m/s²}\approx 1\text{m/s²}

Key Insight: The reason the body accelerates even though it was pushed with "just enough" force is that static friction > kinetic friction. The force required to start motion (static) is greater than the force opposing continued motion (kinetic). So once the body begins moving, the same applied force now exceeds the kinetic friction, producing a net force and hence acceleration of approximately 1 m/sec².