Kinetic Energy : Numerical Problems
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3) Kinetic Energy
Q1. A car of mass 800 kg is moving with a velocity of 20 m/s. Calculate its kinetic energy. āĻĒā§ā§°āĻļā§āĻ¨: āĻāĻāĻ¨ āĻāĻžāĻĄāĻŧā§ā§° āĻā§° ā§Žā§Ļā§Ļ āĻā§āĻāĻŋ āĻā§°ā§ āĻāĻ¤āĻŋ ā§¨ā§Ļ āĻŽāĻŋ/āĻā§āĨ¤ āĻ¤āĻžā§° āĻāĻ¤āĻŋāĻļāĻā§āĻ¤āĻŋ āĻāĻŋāĻŽāĻžāĻ¨ ?
Given / āĻĻāĻŋāĻ¯āĻŧāĻž āĻāĻā§: Mass (m) = 800 kg , Velocity (v) = 20 m/s
Formula / āĻ¸ā§āĻ¤ā§ā§°: Kinetic Energy (KE) = ½ mv² (āĻāĻ¤āĻŋāĻļāĻā§āĻ¤āĻŋ = ½ mv²)
Calculation / āĻāĻŖāĻ¨āĻž:
KE = ½ × 800 × (20)² = ½ × 800 × 400 = 160,000 J
Ans / āĻāĻ¤ā§āĻ¤ā§°: Kinetic Energy = 160,000 Joules (āĻāĻ¤āĻŋāĻļāĻā§āĻ¤āĻŋ = ā§§,ā§Ŧā§Ļ,ā§Ļā§Ļā§Ļ āĻā§āĻ˛)
Q2. A ball of mass 0.5 kg is moving with a speed of 15 m/s. Calculate its kinetic energy. āĻĒā§ā§°āĻļā§āĻ¨: āĻāĻāĻž āĻŦāĻ˛ā§° āĻā§° ā§Ļ.ā§Ģ āĻā§āĻāĻŋ āĻā§°ā§ āĻāĻ¤āĻŋ ā§§ā§Ģ āĻŽāĻŋ/āĻā§āĨ¤ āĻ¤āĻžā§° āĻāĻ¤āĻŋāĻļāĻā§āĻ¤āĻŋ āĻāĻŋāĻŽāĻžāĻ¨ ?
Given / āĻĻāĻŋāĻ¯āĻŧāĻž āĻāĻā§: Mass (m) = 0.5 kg , Velocity (v) = 15 m/s
Formula / āĻ¸ā§āĻ¤ā§ā§°: Kinetic Energy (KE) = ½ mv² (āĻāĻ¤āĻŋāĻļāĻā§āĻ¤āĻŋ = ½ mv²)
Calculation / āĻāĻŖāĻ¨āĻž: KE = ½ × 0.5 × (15)² = 0.25 × 225 = 56.25 J
Ans / āĻāĻ¤ā§āĻ¤ā§°: Kinetic Energy = 56.25 Joules (āĻāĻ¤āĻŋāĻļāĻā§āĻ¤āĻŋ = ā§Ģā§Ŧ.ā§¨ā§Ģ āĻā§āĻ˛)
Q3. A cyclist of mass 60 kg is moving at a speed of 10 m/s. Calculate his kinetic energy.
āĻĒā§ā§°āĻļā§āĻ¨: āĻāĻāĻ¨ āĻāĻžāĻāĻā§āĻ˛ āĻā§°ā§āĻšā§ā§° āĻā§° ā§Ŧā§Ļ āĻā§āĻāĻŋ āĻā§°ā§ āĻāĻ¤āĻŋ ā§§ā§Ļ āĻŽāĻŋ/āĻā§āĨ¤ āĻ¤ā§āĻāĻā§° āĻāĻ¤āĻŋāĻļāĻā§āĻ¤āĻŋ āĻāĻŋāĻŽāĻžāĻ¨?
Given / āĻĻāĻŋāĻ¯āĻŧāĻž āĻāĻā§: Mass (m) = 60 kg , Velocity (v) = 10 m/s
Formula / āĻ¸ā§āĻ¤ā§ā§°: Kinetic Energy (KE) = ½ mv² (āĻāĻ¤āĻŋāĻļāĻā§āĻ¤āĻŋ = ½ mv²)
Calculation / āĻāĻŖāĻ¨āĻž: KE = ½ × 60 × (10)² = ½ × 60 × 100 = 3000 J
Ans / āĻāĻ¤ā§āĻ¤ā§°: Kinetic Energy = 3000 Joules (āĻāĻ¤āĻŋāĻļāĻā§āĻ¤āĻŋ = ā§Šā§Ļā§Ļā§Ļ āĻā§āĻ˛)
Q4. A stone of mass 1.5 kg is moving with a velocity of 12 m/s. Calculate its kinetic energy. āĻĒā§ā§°āĻļā§āĻ¨: āĻāĻāĻž āĻļāĻŋāĻ˛ā§° āĻā§° ā§§.ā§Ģ āĻā§āĻāĻŋ āĻā§°ā§ āĻāĻ¤āĻŋ ā§§ā§¨ āĻŽāĻŋ/āĻā§āĨ¤ āĻ¤āĻžā§° āĻāĻ¤āĻŋāĻļāĻā§āĻ¤āĻŋ āĻāĻŋāĻŽāĻžāĻ¨ ?
Given / āĻĻāĻŋāĻ¯āĻŧāĻž āĻāĻā§: Mass (m) = 1.5 kg , Velocity (v) = 12 m/s
Formula / āĻ¸ā§āĻ¤ā§ā§°: Kinetic Energy (KE) = ½ mv² (āĻāĻ¤āĻŋāĻļāĻā§āĻ¤āĻŋ = ½ mv²)
Calculation / āĻāĻŖāĻ¨āĻž: KE = ½ × 1.5 × (12)² = 0.75 × 144 108 J
Ans / āĻāĻ¤ā§āĻ¤ā§°: Kinetic Energy = 108 Joules (āĻāĻ¤āĻŋāĻļāĻā§āĻ¤āĻŋ = ā§§ā§Ļā§Ž āĻā§āĻ˛)
Q5. A car of mass 900 kg is moving with a velocity of 30 m/s. Calculate its kinetic energy. āĻĒā§ā§°āĻļā§āĻ¨: āĻāĻāĻ¨ āĻāĻžāĻĄāĻŧā§ā§° āĻā§° ā§¯ā§Ļā§Ļ āĻā§āĻāĻŋ āĻā§°ā§ āĻāĻ¤āĻŋ ā§Šā§Ļ āĻŽāĻŋ/āĻā§āĨ¤ āĻ¤āĻžā§° āĻāĻ¤āĻŋāĻļāĻā§āĻ¤āĻŋ āĻāĻŋāĻŽāĻžāĻ¨?
Given / āĻĻāĻŋāĻ¯āĻŧāĻž āĻāĻā§: Mass (m) = 900 kg , Velocity (v) = 30 m/s
Formula / āĻ¸ā§āĻ¤ā§ā§°: Kinetic Energy (KE) = ½ mv² (āĻāĻ¤āĻŋāĻļāĻā§āĻ¤āĻŋ = ½ mv²)
Calculation / āĻāĻŖāĻ¨āĻž: KE = ½ × 900 × (30)² = ½ × 900 × 900 = 405,000 J
Ans / āĻāĻ¤ā§āĻ¤ā§°: Kinetic Energy = 405,000 Joules (āĻāĻ¤āĻŋāĻļāĻā§āĻ¤āĻŋ = ā§Ē,ā§Ļā§Ģ,ā§Ļā§Ļā§Ļ āĻā§āĻ˛)
Q6. A body of mass 2 kg moves with a speed of 5 m/s. āĻĒā§ā§°āĻļā§āĻ¨: āĻāĻāĻž āĻŦāĻ¸ā§āĻ¤ā§ā§° āĻā§° ā§¨ āĻā§āĻāĻŋ āĻā§°ā§ āĻāĻ¤āĻŋ ā§Ģ āĻŽāĻŋ/āĻā§āĨ¤
Formula: KE = ½ mv² (āĻāĻ¤āĻŋāĻļāĻā§āĻ¤āĻŋ = ½ mv²)
Calculation: KE = ½ × 2 × 25 = 25 J
Ans / āĻāĻ¤ā§āĻ¤ā§°: 25 Joules / ā§¨ā§Ģ āĻā§āĻ˛
Q7. A ball of mass 0.4 kg moves at 10 m/s. āĻĒā§ā§°āĻļā§āĻ¨: āĻāĻāĻž āĻŦāĻ˛ā§° āĻā§° ā§Ļ.ā§Ē āĻā§āĻāĻŋ āĻā§°ā§ āĻāĻ¤āĻŋ ā§§ā§Ļ āĻŽāĻŋ/āĻā§āĨ¤
Calculation: KE = ½ × 0.4 × 100 = 20 J
Ans / āĻāĻ¤ā§āĻ¤ā§°: 20 Joules / ā§¨ā§Ļ āĻā§āĻ˛
Q8. A cyclist of mass 50 kg moves at 8 m/s. āĻĒā§ā§°āĻļā§āĻ¨: āĻāĻāĻ¨ āĻāĻžāĻāĻā§āĻ˛ āĻā§°ā§āĻšā§ā§° āĻā§° ā§Ģā§Ļ āĻā§āĻāĻŋ āĻā§°ā§ āĻāĻ¤āĻŋ ā§Ž āĻŽāĻŋ/āĻā§āĨ¤
Calculation: KE = ½ × 50 × 64 = 1600 J
Ans / āĻāĻ¤ā§āĻ¤ā§°: 1600 Joules / ā§§ā§Ŧā§Ļā§Ļ āĻā§āĻ˛
Q9. A stone of mass 1 kg is thrown with a speed of 12 m/s. āĻĒā§ā§°āĻļā§āĻ¨: āĻāĻāĻž āĻļāĻŋāĻ˛ā§° āĻā§° ā§§ āĻā§āĻāĻŋ āĻā§°ā§ āĻāĻ¤āĻŋ ā§§ā§¨ āĻŽāĻŋ/āĻā§āĨ¤
Calculation: KE = ½ × 1 × 144 = 72 J
Ans / āĻāĻ¤ā§āĻ¤ā§°: 72 Joules / ā§ā§¨ āĻā§āĻ˛
Q10: A car of mass 1000 kg moves at 20 m/s. āĻĒā§ā§°āĻļā§āĻ¨: āĻāĻāĻ¨ āĻāĻžāĻĄāĻŧā§ā§° āĻā§° ā§§ā§Ļā§Ļā§Ļ āĻā§āĻāĻŋ āĻā§°ā§ āĻāĻ¤āĻŋ ā§¨ā§Ļ āĻŽāĻŋ/āĻā§āĨ¤
Calculation: KE = ½ × 1000 × 400 = 200000 J
Ans / āĻāĻ¤ā§āĻ¤ā§°: 200,000 Joules / ā§¨,ā§Ļā§Ļ,ā§Ļā§Ļā§Ļ āĻā§āĻ˛
Exam Tips :
- Always write: Given → Formula → Calculation → Answer
- Don’t forget units (J, N, m, kg)
- Steps clearly āĻĻā§āĻā§ā§ąāĻžāĻ˛ā§ full marks āĻĒā§ā§ąāĻž āĻ¯āĻžāĻ¯āĻŧ
- Always write Given, Formula, Calculation, Answer
- Use correct SI units
- Show full steps for full marks
- āĻ¸āĻĻāĻžāĻ¯āĻŧ : āĻĻāĻŋāĻ¯āĻŧāĻž āĻāĻā§ → āĻ¸ā§āĻ¤ā§ā§° → āĻāĻŖāĻ¨āĻž → āĻāĻ¤ā§āĻ¤ā§° āĻ˛āĻŋāĻāĻŋāĻŦ
- Work = Force × Distance → āĻāĻžāĻŽ = āĻŦāĻ˛ × āĻĻā§ā§°āĻ¤ā§āĻŦ
- Potential Energy = mgh → āĻ¸āĻŽā§āĻāĻžā§ąā§āĻ¯ āĻļāĻā§āĻ¤āĻŋ = mgh
- Kinetic Energy = ½ mv² → āĻāĻ¤āĻŋāĻļāĻā§āĻ¤āĻŋ = ½ mv²