Physics · Work, Energy And Power · NEET
On an incline of angle θ, the weight m g is split into two parts: m g sinθ acts along the slope (pulling the block down the slope) and m g cosθ acts perpendicular to the slope (pressing into the surface). The surface pushes back with the normal force N, and this balances only the perpendicular part, so N = m g cosθ (not m g). Because friction f = μN, this means f = μ m g cosθ. Students who use N = m g get every incline-friction problem wrong. This is the single most tested idea on inclines for NEET.
Kinetic friction always acts opposite to the direction the object is moving. Work is W = f d cosφ, where φ is the angle between the force and the displacement. For friction, φ = 180°, so cos180° = -1 and W = -f d. So work done BY friction is negative (it removes kinetic energy as heat). Note the wording: work done BY friction is negative, but work you do AGAINST friction is positive. They are equal in size, opposite in sign.
The magnitude is the same each way (f = μ m g cosθ over the same distance d), but friction is a non-conservative force, so over a full up-and-down trip it does NOT cancel out. Going up, friction removes energy; coming down, friction again removes energy. Total heat lost over a round trip = 2 × μ m g cosθ × d. This is why friction work depends on the path length, unlike gravity.
Step 1: Find the normal force N = m g cosθ. Step 2: Find friction force f = μN = μ m g cosθ. Step 3: Multiply by the distance moved along the slope, d: W_against_friction = μ m g cosθ × d. If the block also rises, the total work you supply to push it up = m g d sinθ (against gravity) + μ m g cosθ × d (against friction). Keep gravity and friction as separate terms.
No. Gravity is a conservative force, so the work done against it depends only on the vertical height gained, W = m g h = m g d sinθ, no matter which path or slope angle you take to reach that height. A gentle long ramp and a steep short ramp to the same height need the same work against gravity. Only the friction part changes with path length. This is why a longer, gentler ramp still costs more total work when friction is present.
A particle of mass M moves along a horizontal x-axis from x = 0 to x = L. The coefficient of kinetic friction varies as μk(x) = μ0 - αx, where μ0, α are constants, so that μk(L) = 0. The total work done by the frictional force during the motion is n μ0 M g L. The value of n is:
An electric lift with a maximum load of 2000 kg (lift + passengers) is moving up with a constant speed of 1.5 m/s. The frictional force opposing the motion is 3000 N. The minimum power delivered by the motor to the lift (in watts) is (g = 10 m/s^2):
When an object is shot up a long smooth inclined plane kept at 60° with the horizontal, it travels a distance x1 along the plane. When the inclination is decreased to 30° and the same object is shot with the same velocity, it travels a distance x2. Then x1 : x2 will be:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
W = f × d = μ m g cosθ × d, where μ is the coefficient of kinetic friction, m is mass, g is gravity, θ is the incline angle, and d is the distance travelled along the slope. The cosθ appears because the normal force on an incline is m g cosθ, not m g.
The weight m g is resolved into a component along the slope (m g sinθ) and a component perpendicular to the slope (m g cosθ). The surface only has to support the perpendicular component, so the normal force N = m g cosθ. Since friction depends on N, this directly changes the friction force to μ m g cosθ.
Friction is a non-conservative (dissipative) force. Work done against it depends on the path length, not just the start and end points, and it converts mechanical energy into heat. This is why a block sliding up and back down a rough incline loses energy on both trips.
Add two terms: work against gravity = m g d sinθ (equal to m g h, the height gained), plus work against friction = μ m g cosθ × d. Total applied work = m g d sinθ + μ m g cosθ × d. On a smooth incline the friction term is zero.
They have equal magnitude but opposite sign. Work done BY friction is negative (friction opposes motion and removes energy). Work done AGAINST friction is positive (this is the energy you must supply to overcome it). NEET questions often use these phrases interchangeably, so watch the sign.
