Work Done Calculation Explained

Understanding the concept of work done is fundamental in physics. Work is defined as the energy transferred by a force acting on an object as it moves. Specifically, it is the product of the force component in the direction of motion and the distance moved. In this problem, we are tasked with calculating the work done to move a body against the force of friction on a horizontal plane.

Frictional Force Determination

To calculate the work done, we first need to determine the force that must be overcome. This force is the force of friction. The force of friction depends on the normal force and the coefficient of friction between the body and the plane.

• Given, the mass of the body (m) = 100 kg
• Given, the coefficient of friction ($\mu$) = 0.025

For a body resting on a horizontal plane, the normal force (N) is equal to the weight of the body. Since the options for work done are given in "kg metres", it implies that we should consider the force in kilogram-force (kgf) units, where 1 kgf is the force exerted by a 1 kg mass due to gravity. Therefore, the normal force is:

Normal Force, $N = \text{mass} = 100 \text{ kgf}$

Now, we can calculate the force of friction (f) using the formula:

Force of friction, $f = \mu \times N$

Substituting the given values into the formula:

$f = 0.025 \times 100 \text{ kgf}$

$f = 2.5 \text{ kgf}$

This frictional force is the force that needs to be applied to move the body at a constant velocity along the plane.

Work Done Calculation

Once the frictional force is determined, the work done (W) in moving the body through a certain distance (d) is calculated using the formula:

Work done, $W = \text{Force} \times \text{Distance}$

• The force to be overcome (which is the frictional force) = 2.5 kgf
• Given, the distance (d) = 10 metres

Substituting these values into the work done formula:

$W = 2.5 \text{ kgf} \times 10 \text{ metres}$

$W = 25 \text{ kg metres}$

Thus, the work done in moving the body through a distance of 10 metres along the plane is 25 kg metres.

Summary of Key Parameters and Results

The calculated work done to move the body against friction aligns with the first option provided.