Physics Question of the Month - October 2019: Kinematics; Energy Work & Power

An object reaches a height of 4m above its point of release when thrown vertically upwards. Given that the object´s mass is 0.4kg, calculate its kinetic energy when it is 3m above its point of release using:

(i) Concepts of kinematics; and

(ii) Concepts of energy work and power.

(i) Using Concepts of Kinematics

Motion from 0m to 4m:

Final Velocity = 0 m/s

Initial Velocity = Unknown

Acceleration = -10 m s^-2

Displacement = 4 m

(Final Velocity)^2 = (Initial Velocity)^2 + 2(Acceleration)(Displacement)

(0)^2 = (Initial Velocity)^2 + 2(-10)(4)

0 = (Initial Velocity)^2 – 80

(Initial Velocity)^2 = 80

Initial Velocity = 8.9443 m/s

Motion from 0m to 3m:

Final Velocity = Unknown

Initial Velocity = 8.9443 m/s

Acceleration = -10 m s^-2

Displacement = 3 m

(Final Velocity)^2 = (Initial Velocity)^2 + 2(Acceleration)(Displacement)

(Final Velocity)^2 = (8.9443)^2 + 2(-10)(3)

(Final Velocity)^2 = 80 – 60

(Final Velocity)^2 = 20

Final Velocity = 4.4721 m/s

Kinetic Energy = 0.5 x Mass x Velocity^2

Kinetic Energy = 0.5 x 0.4 x 20

Kinetic Energy = 4 J

(ii) Using concepts from energy work and power

Motion from 0m to 4m:

∆Gravitational Potential Energy = Mass x Gravitational Field Strength x ∆Height

∆Gravitational Potential Energy = 0.4 x 10 x 4

∆Gravitational Potential Energy = 16 J

Motion from 0m to 3m:

∆Gravitational Potential Energy = Mass x Gravitational Field Strength x ∆Height

∆Gravitational Potential Energy = 0.4 x 10 x 3

∆Gravitational Potential Energy = 12 J

Motion from 3m to 4m:

Due to the Law of Conservation of Energy,

Loss in Kinetic Energy = Gain in Gravitational Potential Energy

Loss in Kinetic Energy = 16 – 12

Loss in Kinetic Energy = 4 J

Velocity of Object at 4m = 0 m/s (due to maximum height being reached)

Kinetic Energy of Object at 4m = 0.5 x Mass x Velocity^2

Kinetic Energy of Object at 4m = 0.5 x 0.4 x 0^2 = 0 J

Kinetic Energy of Object at 3m in Height = (Loss in Kinetic Energy when moving from 3m to 4m) + (Kinetic Energy at 4m in Height)

Kinetic Energy of Object at 3m in Height = 4 + 0 = 4 J