On the horizontal surface of a truck ( μ = 0.6), a block of mass 1 kg is placed. If the truck is accelerating at the rate of 5m/sec then frictional force on the block will be

The correct answer is 5 N.

When a block rests on the surface of an accelerating truck, friction is the only horizontal force available to accelerate the block. Before jumping to the coefficient of friction, we must first check whether the block actually slips on the truck's surface or moves along with it.

Step 1: Find the Maximum Static Friction Force

The maximum friction the surface can provide is given by:

f_{\max }=\mu \times m\times g

Substituting the values (μ = 0.6, m = 1 kg, g = 10 m/s²):

f_{\max }=0.6\times 1\times 10=6\text{N}

Step 2: Find the Force Required to Keep the Block Moving with the Truck

For the block to accelerate at the same rate as the truck (5 m/s²), the friction force needed is:

f_{\mathrm{required}}=m\times a=1\times 5=5\text{N}

Step 3: Compare Required Force vs. Maximum Available Friction

This is the key decision step:

f_{\mathrm{required}}=5\text{N}<f_{\max }=6\text{N}

Since the required friction force (5 N) is less than the maximum static friction (6 N), the block does not slip on the truck. It moves together with the truck.

Step 4: Conclude the Actual Friction Force

Friction is a self-adjusting force. It only provides as much force as is actually needed. Since only 5 N is needed to give the 1 kg block an acceleration of 5 m/s², the static friction acts at exactly 5 N — not at its maximum value of 6 N.

⚠️ Common Mistake to Avoid: Many students directly calculate f = μmg = 6 N. This would only be correct if the block were sliding (kinetic friction). Since the block is not sliding, the friction force equals the required force to produce the same acceleration, which is 5 N.

Therefore, the frictional force on the block = 5 N