Question

A block of mass $100\,g$ slides on a rough horizontal surface. If the speed of the block decreases from $10\,m/s$ to $5\,m/s$ , the thermal energy developed in process is:
A) $3.75\,J$
B) $37.5\,J$
C) $0.375\,J$
D) $0.75\,J$

Answer 1

You can solve this question easily if you try to approach it like this: Calculate the total energy of the block initially, then calculate the final energy. Now, consider if there are some other mediums except heat through which the energy can be lost? You’ll reach at you answer easily if you think about where the lost energy may have gone.

Complete step by step answer:
We’ll be solving the question exactly like we described in the hint section of the solution to the question. Firstly, we will calculate the initial total energy, then we will find the final total energy, the energy that is lost must have lost by being converted into light or heat, etc. So we will account for the lost heat. Now, let’s solve the question.
Firstly, let’s have a look at what the question has given to us:
Mass of the block $\left( m \right) = 100\,g = 0.1\,kg$
Initial velocity of the block $\left( {{v_i}} \right)\, = \,10\,m/s$
Final velocity of the block after the energy loss due to friction $\left( {{v_f}} \right) = 5\,m/s$
Now, let us find the initial total energy of the block:
Potential energy of the block is $0$ . It is so because the block is at the ground level and thus, has no elevation, thus, no potential energy in turn.
Kinetic energy = ${K_i} = \dfrac{1}{2}m{v_i}^2$
Putting in the values of mass and initial velocity as per given to us by the question, we get:
${K_i} = \dfrac{1}{2}\left( {0.1} \right){\left( {10} \right)^2} \\\ {K_i} = 5\,J \\\$
Now, the total energy of the system initially is:
${E_i} = {U_i} + {K_i}$
We have already found out the values of potential and kinetic energies of the block:
${E_i} = 0 + 5J = 5\,J$
Now, let us consider the energies in the final state:
Potential energy is again $0$ since the block hasn’t been lifted up from the ground level.
As for kinetic energy:
${K_f} = \dfrac{1}{2}m{v_f}^2$
Substituting in the values of mass and final velocity of the block as given in the question, we get:
${K_f} = \dfrac{1}{2}\left( {0.1} \right){\left( 5 \right)^2} \\\ {K_f} = 1.25\,J \\\$
Now, let’s find out the total energy in the final state:
${E_f} = {U_f} + {K_f}$
But we have already found out the values of final potential and kinetic energies, substituting them in, we get:
${E_f} = 0 + 1.25\,J = 1.25\,J$
Now, where did the remaining energy go?
We can clearly see that the speed of the block is not high enough to generate light. No other factors of energy loss are as dominating as heat loss.
Thus, the lost energy is converted into heat, this amount is the thermal energy developed in the process:
Thermal energy developed: $H = {E_i} - {E_f}$
We have already found out the values of final and initial energies of the system, substituting them in, we get:
$H = 5 - 1.25 = 3.75\,J$
Hence, the correct option is option (A)

Note: Friction is a non conservative force and it dissipates energy in the form of heat. Many students try to use some other complex methods to find out the thermal energy developed because it is a fancy word used for a simple “heat generated”. The method that we used is the simplest and the fastest to solve such kinds of questions.