Question

Six automobiles are initially traveling at the indicated velocities. The automobiles have different masses and velocities. The drivers step on the brakes and all automobiles are brought to rest. Red Car: 1000kg, 10m/s Yellow Car: 2,000kg, 5m/s Blue Car: 500kg, 20m/s Light Blue Car: 1,000kg, 20m/s Green Car: 500kg, 10m/s Purple Car: 4,000kg, 5m/s Part A Rank these automobiles based on the magnitude of their momentum before the brakes are applied, from largest to smallest. Rank from largest to smallest. To rank items as equivalent, overlap them. Part B Rank these automobiles based on the magnitude of the impulse needed to stop them, from largest to smallest. Rank from largest to smallest. To rank items as equivalent, overlap them. Part C Rank the automobiles based on the magnitude of the force needed to stop them, from largest to smallest. Rank from largest to smallest. To rank items as equivalent, overlap them.

Answer 1

Answer:

Part a)

Purple car = Light Blue car  > (Red car = Yellow Car = Blue car) > Green Car

Part b)

Purple car = Light Blue car  > (Red car = Yellow Car = Blue car) > Green Car

Part c)

Purple car = Light Blue car  > (Red car = Yellow Car = Blue car) > Green Car

Explanation:

Red car

mass = 1000 kg

speed = 10 m/s

Yellow car

mass = 2000 kg

speed = 5 m/s

Blue car

mass = 500 kg

speed = 20 m/s

Light Blue car

mass = 1000 kg

speed = 20 m/s

Green car

mass = 500 kg

speed = 10 m/s

Purple car

mass = 4000 kg

speed = 5 m/s

Part a)

Now we know that momentum of each car is product of mass and velocity

so we will have

Red Car

$P_1 = m v$

$P_1 = (1000)(10)$

$P_1 = 10^4 kg m/s$

Yellow Car

$P_2 = m v$

$P_2 = (2000)(5)$

$P_2 = 10^4 kg m/s$

Blue Car

$P_3 = m v$

$P_3 = (500)(20)$

$P_3 = 10^4 kg m/s$

Light Blue Car

$P_4 = m v$

$P_4 = (1000)(20)$

$P_4 = 2\times 10^4 kg m/s$

Green Car

$P_5 = m v$

$P_5 = (500)(10)$

$P_5 = 5 \times 10^3 kg m/s$

Purple Car

$P_6 = m v$

$P_6 = (4000)(5)$

$P_6 = 2\times 10^4 kg m/s$

So the momentum is given as

Purple car = Light Blue car  > (Red car = Yellow Car = Blue car) > Green Car

Part b)

Impulse is given as change in momentum so here we can say that final momentum of all the cars will be zero as they all stops and hence the impulse is same as initial momentum of the car

so the order of impulse from largest to least is given as

Purple car = Light Blue car  > (Red car = Yellow Car = Blue car) > Green Car

Part c)

Force is defined as rate of change in momentum

Now let say all cars will stop in same time interval

so we will have

$Force = \frac{impulse}{time}$

so we will have

force is in same order as that of impulse

so it is given as

Purple car = Light Blue car  > (Red car = Yellow Car = Blue car) > Green Car

Answer 2

The ranking of the cars from the largest to smallest based on the linear momentum, size of impulse and force needed to stop them is,

Light blue car = Purple car > Red car = Yellow car =  Blue car > Green car

The linear momentum of each car is calculated as follows;

P = mu

where;

• m is the mass of the automobile
• u is linear speed of the automobile

The linear momentum of the Red car is calculated as;

P = 1000 x 10 = 10, 000 kg.m/s

The linear momentum of the Yellow car is calculated as;

P = 2,000 x 5 = 10,000 kg.m/s

The linear momentum of the Blue car is calculated as;

P = 500 x 20 = 10,000 kg.m/s

The linear momentum of the Light blue car is calculated as;

P = 1,000 x 20 = 20,000 kgm/s

The linear momentum of the Green car is calculated as;

P = 500 x 10 = 5,000 kg.m/s

The linear momentum of the Purple car is calculated as;

P = 4,000 x 5 = 20,000 kg.m/s

Impulse is defined as the change in linear momentum;

J = ΔP

J = m(u - v)

where;

• J is the impulse needed to stop each car
• v is the final velocity of the cars when they stop = 0

J = mu = P

The force needed to stop each car is directly proportional to the impulse needed to stop the car.

Ft = J

where;

F is force needed to stop each car

t is the time of motion

Thus, we can conclude that the linear momentum of each car is directly proportional to the impulse and force needed to stop it.

P ∝ J ∝ F

Ranking the cars from the largest to smallest based on the linear momentum, size of impulse and force needed to stop them;

Light blue car = Purple car > Red car = Yellow car =  Blue car > Green car

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