Sam pushes crates starting form rest across the floor of his classroom for 3 s with a net force as shown above. For each crate, rank the following from greatest to least: A 100N/30kg, B 75N/20kg C 50N/10kg
1. Impulse delivered
2. Change in momentum
3. Final speed
4. Momentum in 3s
This is what I have so far:
1. Formula I=Ft: A) I=100N(3s) 300Ns B) I=75N(3s)=225Ns C) I=50N(3s)=150Ns
2. Formula F=ma: A) F=100N(30kg)=3000Nkg B) F=75N(20kg)= 1500Nkg C) F=50N(10kg)=500Nkg
I cannot figure out how to find 3 and 4. If you could please write the formula for the answer
I will try crate 1
m = 30 kg
F = 100 N
1. impulse = F t = 100 * 3 = 300 Ns yes
2. Force = change in momentum/time
and initial momentum = 0
so
100 = change in momentum/3
so
change in momentum = 300 kg m/s = Ns
(by the way if there is a difference between change of momentum and impluse I do not know it.)
3. m v = momentum = 300
so v = 300/30 = 10 m/s
4. same as answers 1. and 2. since initial momentum is zero (at rest)
To find the answers for 3) Final speed and 4) Momentum in 3s, we need to make use of Newton's second law of motion and the formula for momentum.
3) Final speed:
The equation we'll use is:
Final speed = Initial speed + (Net Force / Mass) * Time
Since the crates start from rest, their initial speed is zero. We can substitute the values into the equation for each crate:
For crate A:
Mass = 30kg
Net Force = 100N
Time = 3s
Final speed of crate A = 0 + (100N / 30kg) * 3s
For crate B:
Mass = 20kg
Net Force = 75N
Time = 3s
Final speed of crate B = 0 + (75N / 20kg) * 3s
For crate C:
Mass = 10kg
Net Force = 50N
Time = 3s
Final speed of crate C = 0 + (50N / 10kg) * 3s
4) Momentum in 3s:
The formula for momentum is given by:
Momentum = Mass * Velocity
We can calculate the momentum of each crate using the final speed calculated in step 3 above:
For crate A:
Mass = 30kg
Velocity = Final speed of crate A
Momentum of crate A = 30kg * Final speed of crate A
For crate B:
Mass = 20kg
Velocity = Final speed of crate B
Momentum of crate B = 20kg * Final speed of crate B
For crate C:
Mass = 10kg
Velocity = Final speed of crate C
Momentum of crate C = 10kg * Final speed of crate C
After calculating the final speed and momentum for each crate, you can rank them from greatest to least according to the given values.
To find the answers to questions 3 and 4, we need to use the concept of impulse and momentum.
3. Final speed:
To find the final speed of each crate, we can use the equation:
Final speed = Initial speed + (Impulse / Mass)
Since the crates start from rest, the initial speed is 0m/s. We can use the impulse values we calculated earlier and divide them by the respective masses to find the final speed for each crate:
For crate A: Final speed = 0 + (300Ns / 30kg) = 10m/s
For crate B: Final speed = 0 + (225Ns / 20kg) = 11.25m/s
For crate C: Final speed = 0 + (150Ns / 10kg) = 15m/s
So the ranking of the final speeds from greatest to least is: C, B, A.
4. Momentum in 3 seconds:
To find the momentum of each crate after 3 seconds, we can use the equation:
Momentum = Mass × Final speed
Using the final speed values calculated above for each crate, we can multiply them by their respective masses:
For crate A: Momentum = 30kg × 10m/s = 300kg·m/s
For crate B: Momentum = 20kg × 11.25m/s = 225kg·m/s
For crate C: Momentum = 10kg × 15m/s = 150kg·m/s
So the ranking of the momentum values from greatest to least is: A, B, C.