A block of mass 50 kg slides over a horizontal distance of 1 m. If the coefficient of friction between their surfaces is 0.2, then work done against friction is

The correct answer is 98 J.

To find the work done against friction, we need to first calculate the frictional force acting on the block, and then use the work-energy relationship.

Step 1: Identify the given values

Mass of the block: m = 50 kg
Horizontal distance: d = 1 m
Coefficient of kinetic friction: μ = 0.2
Acceleration due to gravity: g = 9.8 m/s²

Step 2: Find the Normal Force (N)

Since the block slides over a horizontal surface, the normal force is equal to the weight of the block. There is no vertical acceleration, so:

N=m\times g

N=50\times 9.8

N=490\text{N}

Step 3: Calculate the Force of Friction (f)

The kinetic friction force is given by:

f=\mu \times N

f=0.2\times 490

f=98\text{N}

Step 4: Calculate the Work Done Against Friction (W)

Work done against friction is the energy used to overcome the frictional force over the given distance. It is given by:

W=f\times d

W=98\times 1

W=98\text{J}

Conclusion:
The work done against friction is 98 J. This energy is not lost entirely — it is converted into heat energy at the contact surface between the block and the horizontal surface, which is a classic example of the conversion of mechanical energy into thermal energy due to friction.