Relationship between momentum and kinetic energy

ke = 1/2 * m * V^2 kinetic energy = 1/2 * mass * velocity squared

ke = 1/2 * m * v * v kinetic energy = 1/2 * mass * velocity * velocity

p = m * v momentum = mass * velocity

ke = (m * v) * (1/2 * v) kinetic energy = momentum * 1/2 * velocity

An object's kinetic energy due to its motion is equal to the product of its momentum

and 1/2 its velocity. ke = p * (1/2 * v)

also

An object's momentum is the quotient of the division of its kinetic energy

by 1/2 of its velocity. p = ke / (1/2 * v)

... ... ... ... ... ... ...

... ... ... ... ... ... ...

scenario 0

force = 3 N

time = 25 seconds

mass = zero

force = mass times acceleration

momentum = mass times velocity

momentum = zero

... ... ... ... ... ... ...

scenario 1

force = 3 N

time = 25 seconds

mass = 15 kg

force = mass times acceleration

momentum = mass times velocity

momentum = 15 kg * 5m/s .. "75 momentum"

kinetic energy = 1/2 * m * v^2

velocity = 5 m/s

because

1 Newtons of force will cause 1 kg to accelerate to 1 meter / second in 1

second (by definition)

and

1 Newton of force will cause 15 kg to accelerate to 1/15 (0.0666666666666666

6666666666666667) meter / second in 1 second

and

3 Newtons of force will cause 15 kg to accelerate to ( 0.0666... times 3) which is

0.2 meter/second in 1 second

and

3 Newtons of force will cause 15 kg to accelerate to, 0.2 times 25, in 25 seconds

and

this is equal to 5 meters per second velocity (0.2 * 25 = 5)

A 15 kg mass moving at 5 m/s has 187.5 joules of kinetic energy

Ek = 1/2 * Mass * Velocity ^2

kinetic energy = 1/2 * 15 kg * 5m/s^2 ... 1/2 * 15 kg * 25 = 187.5 joules

5 m/s ^2 = 25

15 kg * 25 = 375

375 / 2 = 187.5 joules

An object's momentum is the quotient of the division of its kinetic energy

by 1/2 of its velocity. p = ke / (1/2 * v)

187.5 joules / 1/2 * 5 m/s as in 187.5 joules / 2.5 m/s as in "75 momentum"

momentum = mass * velocity

15 kg of mass * 5 m/s = "75 momentum"

Momentum = force * time

3 Newtons * 25 seconds = "75 momentum"

... ... ... ... ... ... ...

... ... ... ... ... ... ...

scenario 2

force = 3 N

time = 25 seconds

mass = 4 kg

force = mass times acceleration

momentum = mass times velocity

momentum = zero

... ... ... ... ... ... ...

force = 3 N

time = 25 seconds

mass = 4 kg

momentum = 4 kg * 0.75 m/s = 3

kinetic energy = 1/2 * m * v^2

velocity = 18.75 m/s

because

1 Newtons of force will cause 1 kg to accelerate to 1 meter / second in 1

second (by definition)

and

1 Newton of force will cause 4 kg to accelerate to 1/4 (0.25) meter / second in 1 second

and

3 Newtons of force will cause 4 kg to accelerate to 0.25 times 3 which is

0.75 meter/second in 1 second

and

3 Newtons of force will cause 4 kg to accelerate to 0.75 times 25, in 25 seconds

and

this is equal to 18.75 meters per second velocity (0.75 * 25 = 18.75)

... ... ... ... ...

A 4 kg mass moving at 18.75 m/s has ? joules of kinetic energy

Ek = 1/2 * Mass * Velocity ^2

kinetic energy = 1/2 * 4 kg * 18.75 m/s^2 ... 1/2 * 4 kg * 351.5625 = 703.125 joules

18.75 m/s ^2 = 351.5625

4 kg * 351.5625 = 1406.25

1406.25 / 2 = 703.125 joules

An object's momentum is the quotient of the division of its kinetic energy

by 1/2 of its velocity. p = ke / (1/2 * v)

703.125 joules / 1/2 * 18.75 m/s or stated as 703.125 joules / 9.375 m/s or stated

as in "75 momentum"

momentum = mass * velocity

4 kg of mass * 18.75 m/s = "75 momentum"

Momentum = force * time

3 Newtons * 25 seconds = "75 momentum"

Momentum = force * time

cool !