Question

A 102kg car moving with a velocity of 12m/s collides with a 210kg truck moving in the opposite direction. Assume that both vehicles end with zero speed.What is the cars momentum before the collision?What was the change in the car’s momentum?What was the change in the truck’s momentum?What was the truck’s original momentum?How fast was the truck moving before the collision?

Answer 1

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:

`P=m* v`

Where:

m = 102 kg

v = 12 m/s

`P=102*12=1224kg.m\text{ /s}`

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:

`\begin{gathered} \Delta P=mv_f-mv_i \\ \\ \Delta P=m(v_f-v_i) \\ \\ \Delta P=102(0-12) \\ \\ \Delta P=-1224kg\cdot(m)/(s) \end{gathered}`

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:

`P=m_1v_1-m_2v_2`

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:

`\begin{gathered} 0=(102*12)-(210* v_2) \\ \\ 0=1224-210v_2_{} \\ \\ 210v_2=1224 \\ \\ v_2=(1224)/(210) \\ \\ v_2=5.83\text{ m/s} \end{gathered}`

The initial velocity of the truck is = 5.83 m/s

To find the change in the truck's momentum, we have:

`\begin{gathered} \Delta P=210(0-5.83) \\ \\ \Delta P=-1224\text{ m/s} \end{gathered}`

The change in momentum of the truck is -1224 m/s.

• (e). What was the truck’s original momentum?

`\begin{gathered} P=210*5.83 \\ \\ P=1224\text{ m/s} \end{gathered}`

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