Respuesta :
Answer:
47.04 N*s or 47.04 kg*m/s
Explanation:
momentum is equal to mass times velocity the mass stays constant so we need to find the final and initial velocity. We are given the initial velocity of 4.0 m/s so plugging that into the momentum formula that is an initial momentum of 48 kg*m/s.
Now we can solve for the final velocity by using the kinematic formulas. First we must find the net force which is the friction so friction is equal to coefficient * normal force with the normal force equaling the force of gravity. Therefore we get a frictional force of 23.52 N
Now to find the acceleration we use newtons second a=f/m and get acceleration is equal to 1.96 m/s^2.
Now just find the Vfinal; Vfinal= Viinital +acceleration* time.
since the acceleration is negative we get 0.08m/s. Now just plug in to find final momentum of .96kgm/s. Then find the difference to be -47.04 kg*m/s.
Alternatively if you know that impulse is equal to change in momentum and equals force times time. We know the friction force is 23.52N in the negative direction applied for 2 seconds so we once again get -47.04 N*s which is the same unit as kg*m/s
however since the question just asks for magnitude we take the absolute value and get 47.04 N*s
The magnitude of the change in momentum of the box during this time is most nearly -48 kgm/s
To calculate the change in momentum of the box,
- First, we need to calculate the final speed.
Using
S = (v+u)t/2........................ Equation 1
Where:
- S = distance moved by the box
- v = Final velocity of the box
- u = Initial velocity of the box
- t = time
Given:
- S = 4 m, u = 4 m/s, t = 2
Substitute these values into equation 1 and solve for v
4 = (v+4)2/2
v = 0 m/s.
- Secondly, we use the formula of change in momentum
M = m(v-u).................... Equation 2
Where:
- M = change in momentum
- m = mass of the box
- v = final velocity of the box
- u = initial velocity of the box
Given:
- m = 12 kg
- u = 4 m/s
- v = 0 m/s (calculated)
Substitute these values into equation 2
- M = 12(0-4)
- M = 12(-4)
- M = -48 kgm/s
Hence, The change in momentum of the box is -48 kgm/s
Learn more about Final velocity here: https://brainly.com/question/18762601
