Answer: a) 8 Kg m/s b) 16 Kg m/s c) 24 Kg m/s d) 16 J e) 128 J f) 144 J
g) 4 s
Explanation:
a) As momentum by definition is the product of mass times the velocity (is a vector quantity), we can write in this case the following:
pi = m. v₀ = 2 Kg . 4 m/s = 8 Kg. m/s
b) In order to get the change in momentum, we need to get first the final speed of the object.
As we have the total distance travelled, and we could find the acceleration, we could use a kinematic equation to solve the question, but later we will need the kinetic energy, it would be better to apply the work-energy theorem, and calculate ΔK as the work done by external force F, as follows:
ΔK = F . d = 1/2 m (vf² - v₀²)
As we know F, d, m, and v₀, we can solve the equation above for vf:
vf = 12 m/s
So, we can compute the final momentum as follows:
pf = m. vf = 2 Kg. 12 m/s = 24 Kg. m/s
Finally, we can find the change in momentum, as the difference between the final momentum and the initial one, calculated in a):
Δp = pf - pi = 24 Kg. m/s - 8 Kg. m/s = 16 Kg. m/s
c) As we have already found, final momentum is as follows:
pf = m . vf = 2 Kg. 12 m/s = 24 Kg. m/s
d) By definition the initial kinetic energy of the box is as follows:
Ki = 1/2 m v₀² = 1/2. 2 Kg .4² m²/s² = 16 J
e) We can find the change in the kinetic energy taking directly the difference between the final and initial ones, as follows:
ΔK = Kf - Ki = 1/2. 2 Kg (12² - 4²) m²/s² = 128 J
f) From above, we have Kf = 1/2 m. vf² = 1/2 . 2 Kg. 12² m²/s² = 144 J
g) As we know the magnitude of F, and the value of m, we can find the acceleration (assumed constant) , applying Newton's Second Law, as follows:
Fext = m .a ⇒ a = F/m = 4 N / 2 Kg = 2 m/s²
Appying the definition of acceleration, we can solve for t, as follows:
t = (vf-v₀) / a = (12 m/s - 4 m/s) / 2 m/s² = 4 s
