Question

A block of mass 100 kg slides over a distance of 10 m on a horizontal surface. If the coefficient of friction between the surfaces is 0.4, then the work done against friction (in J) is:

• A. 4500 J
• B. 50000 J
• C. 4200 J
• D. 4000 J

Answer 1

The Correct Option is D

The work done against friction when a block slides over a surface is calculated using the formula:

\(W = f \cdot d\)

where:

• \(W\) represents the work done against friction (in Joules, J).
• \(f\) is the force of friction (in Newtons, N).
• \(d\) is the distance over which the force acts (in meters, m).

The force of friction \(f\) is determined by the formula:

\(f = \mu \cdot N\)

where:

• \(\mu\) is the coefficient of friction.
• \(N\) is the normal force (in Newtons, N). On a horizontal surface, this equals the block's weight, meaning \(N = m \cdot g\), with \(m\) being the mass (in kg) and \(g\) being the acceleration due to gravity (approximately \(9.8 \, \text{m/s}^2\)).

Substituting the values yields:

\(N = 100 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 980 \, \text{N}\)

The force of friction is then calculated as:

\(f = 0.4 \times 980 \, \text{N} = 392 \, \text{N}\)

The work done against friction is:

\(W = 392 \, \text{N} \times 10 \, \text{m} = 3920 \, \text{J}\)

Given that the provided options and answer round the value to 4000 J, the closest correct approximation is:

4000 J

Consequently, the correct answer is 4000 J.