Answer :
Given:
Mass of car = 102 kg
Velocity of car = 12 m/s
Mass of truck = 210 kg.
Assuming that both vehicles end with zero speed after collison, let's solve for the followinG.
• (b). What is the cars momentum before the collision?
To find the car's momentum before collision, apply the formula:
[tex]P=m\times v[/tex]Where:
m = 102 kg
v = 12 m/s
[tex]P=102\times12=1224kg.m\text{ /s}[/tex]The car's momentum before collision is 1224 kg.m/s
• (c). What was the change in the car’s momentum?
Since the car will end with zero speed, the final velocity, vf = 0 m/s
To find the change in momentum, we have:
[tex]\begin{gathered} \Delta P=mv_f-mv_i \\ \\ \Delta P=m(v_f-v_i) \\ \\ \Delta P=102(0-12) \\ \\ \Delta P=-1224kg\cdot\frac{m}{s} \end{gathered}[/tex]The change in the car's momentum is -1224 kg. m/s
• (d). What was the change in the truck’s momentum?
Where:
mass of truck = 210 kg
Since both vehicles stopped after collision, the final momentum will be zero.
Now, apply the equation:
[tex]P=m_1v_1-m_2v_2[/tex]Where:
P = 0
m1 is the mass of car
v1 is the initial velocity of the car
m2 is the mass of the truck
v2 is the initial velocity of the truck.
Thus, we have:
[tex]\begin{gathered} 0=(102\times12)-(210\times v_2) \\ \\ 0=1224-210v_2_{} \\ \\ 210v_2=1224 \\ \\ v_2=\frac{1224}{210} \\ \\ v_2=5.83\text{ m/s} \end{gathered}[/tex]The initial velocity of the truck is = 5.83 m/s
To find the change in the truck's momentum, we have:
[tex]\begin{gathered} \Delta P=210(0-5.83) \\ \\ \Delta P=-1224\text{ m/s} \end{gathered}[/tex]The change in momentum of the truck is -1224 m/s.
• (e). What was the truck’s original momentum?
[tex]\begin{gathered} P=210\times5.83 \\ \\ P=1224\text{ m/s} \end{gathered}[/tex]The truck's original momentum is 1224 kg.m/s
• (f). , How fast was the truck moving before the collision?
From the calculation in part D, we can see the velocity of the truck before collision is 5.83 m/s
ANSWER:
• (b). 1224 kg. m/s
,• (c). -1224 kg.m/s
,• (d). -1224 kg m/s
,• (e). 1224 kg.m/s
,• (f). 5.83 m/s