Questions: Mechanical Energy and Non-Conservative Forces

Question 1

A block slides down a rough ramp with friction. Compared to a frictionless ramp of identical height, which of the following is true at the bottom?

• A. Total energy (mechanical + thermal) is less on the rough ramp because friction removed energy from the system
• B. The block has less kinetic energy on the rough ramp, and the 'lost' mechanical energy has been permanently converted to thermal energy
• C. The block has less kinetic energy on the rough ramp, but this energy is stored temporarily in the rough surface and can be recovered
• D. The block has the same kinetic energy on both ramps because gravity converts the same potential energy in both cases

Answer: (B)

Friction does negative work on the block, permanently converting mechanical energy to thermal energy (microscopic random motion of atoms in the contacting surfaces). The block arrives with less kinetic energy — by exactly the amount of thermal energy generated. Total energy is conserved: the mechanical energy that disappeared reappears as heat. Option C is incorrect: friction-generated heat cannot spontaneously reconvert to mechanical energy.

Question 2

Using the modified conservation law E_mech,f = E_mech,i + W_nc, what is the sign of W_nc for a block sliding along a rough horizontal surface that comes to rest?

• A. W_nc = 0 because no conservative forces act on the horizontal surface
• B. W_nc > 0 because friction adds energy to the system from the surface
• C. W_nc < 0 because friction does negative work on the block, removing mechanical energy
• D. W_nc is undefined because the block stops, meaning there is no net displacement

Answer: (C)

Friction opposes motion, so the friction force and displacement point in opposite directions — their dot product is negative. W_nc = F_friction · d · cos(180°) = −F_friction · d < 0. The negative W_nc means final mechanical energy is less than initial, accounting for the kinetic energy converted to heat as the block decelerates. The block has displacement (it slides before stopping), so W_nc is well-defined and negative.

Question 3

When non-conservative forces like friction act on a system, the total energy of the universe (including thermal energy) decreases.

• T. True
• F. False

Answer: False

Total energy is ALWAYS conserved — this is the first law of thermodynamics. What decreases is the mechanical energy (KE + PE) of the system, not the total energy. The mechanical energy that disappears converts to thermal energy: the random kinetic energy of atoms in the surfaces in contact. The total energy (mechanical + thermal) remains constant. Only the form changes.

Question 4

Non-conservative forces are called 'non-conservative' because the work they do on an object depends on the path taken, not just the starting and ending positions.

• T. True
• F. False

Answer: True

Conservative forces (gravity, springs) do work that depends only on initial and final positions — you can define a potential energy function for them. Non-conservative forces like friction do work that depends on the entire path: a longer or rougher path means more friction work, even between the same two endpoints. This path-dependence is precisely why we cannot assign a potential energy to friction, and why the standard conservation equation (using only potential energy) is insufficient.

Question 5

Explain why total energy is conserved when friction acts on a sliding block, even though the block slows down and loses mechanical energy.

Model answer: Total energy is conserved because the mechanical energy lost by the block is not destroyed — it is converted into thermal energy in the surfaces in contact. Friction generates heat through microscopic deformation and vibration of atoms at the sliding interface. The kinetic energy the block loses equals exactly the thermal energy gained by the surfaces. Mechanical energy decreases; thermal energy increases by the same amount; their sum remains constant.

This is the key distinction between 'energy conservation' (always true) and 'mechanical energy conservation' (only true for conservative-force systems). The modified law E_mech,f = E_mech,i + W_nc is careful bookkeeping: W_nc is negative (energy leaves the mechanical account) and that amount is deposited into the thermal account. Total balance is always zero change.