UPCAT Physics — Work, Energy & ImpulseFlash Cards

A force of 50 N is applied to move a box 10 meters horizontally. Calculate the work done.

Formula: W = F × d × cos θ Step 1: Identify values - F = 50 N, d = 10 m, θ = 0° (horizontal) Step 2: W = 50 N × 10 m × cos(0°) Step 3: W = 50 × 10 × 1 = 500 J Answer: 500 J

What is the definition of work in physics and what are its units?

Work is the energy transferred when a force acts on an object and causes displacement in the direction of the force. Formula: W = F × d × cos θ, where θ is the angle between force and displacement. SI unit: Joule (J). 1 Joule = 1 Newton-meter.

A 2 kg ball is thrown with a velocity of 15 m/s. Find its kinetic energy.

Formula: KE = ½mv² Step 1: Identify values - m = 2 kg, v = 15 m/s Step 2: KE = ½ × 2 kg × (15 m/s)² Step 3: KE = 1 × 225 = 225 J Answer: 225 J

A book with mass 1.5 kg is placed on a shelf 3 meters high. Calculate its gravitational potential energy.

Formula: PE = mgh Step 1: Identify values - m = 1.5 kg, g = 9.8 m/s², h = 3 m Step 2: PE = 1.5 kg × 9.8 m/s² × 3 m Step 3: PE = 44.1 J Answer: 44.1 J

Why does a roller coaster have maximum kinetic energy at the bottom of a hill?

At the bottom, the roller coaster has minimum potential energy (lowest height) and maximum speed due to energy conservation. As PE decreases during descent, it converts to KE. Total mechanical energy (KE + PE) remains constant, so minimum PE means maximum KE.

State the Law of Conservation of Energy and give an example.

Energy cannot be created or destroyed, only converted from one form to another. The total energy in an isolated system remains constant. Example: A pendulum converts PE to KE and back - at the highest points PE is maximum and KE is zero, at the lowest point KE is maximum and PE is minimum.

A 0.5 kg ball moving at 20 m/s hits a wall and bounces back at 15 m/s. Calculate the change in momentum.

Formula: Δp = m(v₂ - v₁) Step 1: m = 0.5 kg, v₁ = +20 m/s, v₂ = -15 m/s (opposite direction) Step 2: Δp = 0.5 kg × (-15 - 20) m/s Step 3: Δp = 0.5 × (-35) = -17.5 kg⋅m/s Answer: -17.5 kg⋅m/s (magnitude = 17.5 kg⋅m/s)

What is impulse and how is it related to momentum?

Impulse is the change in momentum caused by a force acting over time. Formula: J = Ft = Δp = m(v₂ - v₁). Units: Newton-seconds (N⋅s) or kg⋅m/s. Impulse equals the area under a force-time graph. Greater impulse means greater change in motion.

A 1200 kg car traveling at 25 m/s brakes to a stop in 8 seconds. Find the braking force.

Using impulse-momentum theorem: Ft = Δp Step 1: Δp = m(v₂ - v₁) = 1200(0 - 25) = -30,000 kg⋅m/s Step 2: F × 8 s = -30,000 kg⋅m/s Step 3: F = -30,000 ÷ 8 = -3,750 N Answer: 3,750 N (braking force magnitude)

When is work done zero even if force is applied?

Work is zero when: (1) Force is perpendicular to displacement (θ = 90°, cos 90° = 0), (2) No displacement occurs (d = 0), or (3) No force is applied (F = 0). Example: Carrying a bag horizontally - the upward force doesn't do work on horizontal motion.

A spring with spring constant 200 N/m is compressed by 0.3 m. Find the elastic potential energy stored.

Formula: PE_elastic = ½kx² Step 1: k = 200 N/m, x = 0.3 m Step 2: PE = ½ × 200 N/m × (0.3 m)² Step 3: PE = 100 × 0.09 = 9 J Answer: 9 J

What is power and how does it relate to work?

Power is the rate of doing work or transferring energy. Formula: P = W/t or P = Fv (when force and velocity are in same direction). SI unit: Watt (W) = J/s. Higher power means work is done faster, not necessarily more work total.

A machine does 3000 J of work in 10 seconds. Calculate its power output.

Formula: P = W/t Step 1: W = 3000 J, t = 10 s Step 2: P = 3000 J ÷ 10 s Step 3: P = 300 W Answer: 300 W

Why do airbags in cars reduce injury during collisions?

Airbags increase the collision time, reducing the force experienced by passengers. Using J = Ft, for the same impulse (momentum change), longer time means smaller force. This prevents severe injuries that would occur from sudden stops with large forces over short times.

Two objects collide: 3 kg moving at 8 m/s hits stationary 2 kg object. After collision, they stick together. Find their common velocity.

Conservation of momentum: p_initial = p_final Step 1: p_initial = m₁v₁ + m₂v₂ = 3×8 + 2×0 = 24 kg⋅m/s Step 2: p_final = (m₁ + m₂)v = (3 + 2)v = 5v Step 3: 24 = 5v, so v = 4.8 m/s Answer: 4.8 m/s

A 5 kg object falls from rest through a height of 20 m. Find its speed just before hitting the ground (ignore air resistance).

Using energy conservation: PE_initial = KE_final Step 1: PE = mgh = 5 × 9.8 × 20 = 980 J Step 2: KE = ½mv² = 980 J Step 3: ½ × 5 × v² = 980 Step 4: v² = 392, v = 19.8 m/s Answer: 19.8 m/s

What is the work-energy theorem?

The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W_net = ΔKE = KE_final - KE_initial = ½m(v₂² - v₁²). This connects the concepts of work and energy, showing work changes an object's kinetic energy.

A 800 N person climbs stairs 15 m high in 20 seconds. Calculate the power required.

Step 1: Work done against gravity = mgh = Fh = 800 N × 15 m = 12,000 J Step 2: Power = Work/time = 12,000 J ÷ 20 s = 600 W Answer: 600 W Note: This is the minimum power needed to overcome gravity.

What is mechanical energy and when is it conserved?

Mechanical energy is the sum of kinetic and potential energy: E = KE + PE = ½mv² + mgh. It's conserved in the absence of non-conservative forces (like friction, air resistance). Examples: pendulum motion, roller coaster (ignoring friction), projectile motion.

A tennis ball (60 g) is hit with a racket, changing its velocity from 0 to 40 m/s in 0.02 seconds. Find the average force exerted.

Using impulse: F_avg × t = Δp Step 1: m = 0.06 kg, Δv = 40 - 0 = 40 m/s Step 2: Δp = 0.06 × 40 = 2.4 kg⋅m/s Step 3: F_avg = Δp/t = 2.4 ÷ 0.02 = 120 N Answer: 120 N