The velocity of a ball changes from ‹ 8, −5, 0 › m/s to ‹ 7.88, −5.28, 0 › m/s in 0.04 s, due to the gravitational attraction of the Earth and to air resistance. The mass of the ball is 140 grams.
I calculated the acceleration and got <-3,-7,0>
what is the equation to find the rate of change of momentum of the ball?
Force = rate of change of momentum = m a if mass is constant
(7.88 - 8)/.04 = -3
(-5.28+5) /.04 = -7
(0 - 0 ) = 0
so yes
m a = .140 (do it in kg) * that a vector
By the way, Newton 2 is
force = rate of change of momentum
F = m A is the simple version but will not work if mass is not constant (rocket or special relativity for example)
Well, equation-wise, the rate of change of momentum can be determined using the formula:
Rate of Change of Momentum = Mass of the Object × Acceleration
In this case, the mass of the ball is given as 140 grams, but it is usually better to use kilograms for calculations. So, let's convert that into kilograms, which would give us 0.14 kg.
Now, taking the calculated acceleration of <-3, -7, 0> m/s^2, we can use the formula to find the rate of change of momentum:
Rate of Change of Momentum = 0.14 kg × <-3, -7, 0> m/s^2
And voila! That's the equation to find the rate of change of momentum of the ball.
The equation to find the rate of change of momentum of an object is given by the formula:
Rate of change of momentum = mass × acceleration
Given that the mass of the ball is 140 grams and the acceleration is ‹-3, -7, 0› m/s², we can use the equation to calculate the rate of change of momentum.
To convert the mass from grams to kilograms, we divide it by 1000:
Mass = 140 grams ÷ 1000 = 0.14 kilograms
Plugging these values into the equation, we get:
Rate of change of momentum = 0.14 kilograms × ‹-3, -7, 0› m/s²
To calculate the product of a scalar (mass) and a vector (acceleration), we perform scalar multiplication on each component of the vector:
Rate of change of momentum = ‹0.14 × -3, 0.14 × -7, 0.14 × 0› kg • m/s²
Simplifying, we have:
Rate of change of momentum = ‹-0.42, -0.98, 0› kg • m/s²
Therefore, the rate of change of momentum of the ball is ‹-0.42, -0.98, 0› kg • m/s².