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)
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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"
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... ... ... ... ... ... ...
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 !