Understanding Kinetic Energy Equations and Examples
Learn how to rearrange and calculate kinetic energy using the formula KE = 1/2mv^2. Explore the definition, formula representation, solving for mass and velocity, related equations, and practice with calculation examples. Understand how mass and velocity affect kinetic energy in various scenarios.
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Presentation Transcript
Rearranging Kinetic Energy Equation
Learning Objectives I can mathematically rearrange the kinetic energy equation. I can calculate Kinetic Energy using the formula.
Kinetic Energy Definition and Formula The energy an object has due to its motion Formula: KE = 1 2mv2 Kinetic energy is calculated by: Squaring the velocity (v), multiply by the object s mass (m), than divided by 2.
Formula Representation Formula Represents KE = m = mass v = velocity Units Kinetic Energy Joules (J) kilogram (kg) Meter/second (m/s) KE = 1 2mv2
Solve for Mass (m) Solve for Mass (m) KE = 1 2Ke = mv2 __ v2 Step 1 Multiply by 2 on both sides Step 2 Divide by v2 on both sides (2) (2) 2mv2 __ v2 m = 2K? ?2
Solve for Velocity (v) Solve for Velocity (v) KE = 1 2Ke = mv2 __ m Step 1 Multiply by 2 on both sides Step 2 Divide by m on both sides Step 3 Square root both sides 2mv2 __ m (2) (2) 2Ke = v2 m 2?? ? v =
Kinetic Energy Related Equations Kinetic Energy KE = 1 mass height 2mv2m = 2K? 2?? ? v = ?2
Calculation Example #1 A bicycle and rider with a combined mass of 110kg are traveling at a speed of 8m/s. What is the kinetic energy of the bicycle and rider? Given/ Unknown KE = m = v = 8 m/s Work ? KE =1 KE =1 110kg KE =1 2mv2 2110kg (64m2/s2) 2110kg (8m/s)2 KE =1 KE = 3520J 27040J
Calculation Example #2 Find the kinetic energy of a .1kg toy truck moving at a speed of 1.1m/s. Given/ Unknown KE = m = v = 1.1 m/s Work ? KE =1 KE =1 .1kg KE =1 2mv2 2.1kg (1.21m2/s2) 2.1kg (1.1m/s)2 KE =1 KE = .0605J 2.121J
Calculation Example #3 The kinetic energy of a bowling ball traveling at a speed of 4m/s is 50J. Find the mass of the ball. Given/ Unknown KE = m = v = 4 m/s Work 50J 100? 16?2/?2 m =2?? 2(50?) (4?/?)2 ? m = 6.25kg m = m = ?2
Calculation Example #4 A 50kg cheetah has a kinetic energy of 18,000J. How fast is the cheetah running? Given/ Unknown KE = m = v = ? Work 18,000J 2(18,000?) 50?? 36,000? 50?? 2?? ? ? = 720 50kg ? = ? = ? = V = 26.83m/s
