A compact car, mass 705 kg, is moving at 1.00 102 km/h toward the east. Sketch the moving car. Do this on paper. Your instructor may ask you to turn in this work..
(a) Find the magnitude and direction of its momentum. Draw an arrow on your sketch showing the momentum.
kg · m/s
(b) A second car, with a mass of 2385 kg, has the same momentum. What is its velocity?
km/h (in the same direction)
To find the magnitude and direction of the momentum of the compact car, we can use the formula:
Momentum = mass * velocity
Where the mass of the compact car is given as 705 kg and the velocity is given as 102 km/h. However, we need to convert the velocity to m/s since the SI unit for momentum is kg·m/s.
To convert km/h to m/s, divide the velocity by 3.6:
102 km/h ÷ 3.6 = 28.33 m/s (rounded to two decimal places)
Now, we can calculate the momentum:
Momentum = 705 kg * 28.33 m/s = 19993.65 kg·m/s (rounded to two decimal places)
The magnitude of the momentum is approximately 19993.65 kg·m/s.
To determine the direction of the momentum, we look at the given information, which states that the car is moving toward the east. Therefore, the momentum vector would point towards the east on the sketch. Draw an arrow on your sketch in the eastward direction to represent the momentum.
Now, let's move on to the second part of the question, where we have a second car with a mass of 2385 kg and the same momentum.
To find the velocity of the second car, we rearrange the momentum formula:
Velocity = Momentum / mass
Substituting the values:
Velocity = 19993.65 kg·m/s / 2385 kg = 8.38 m/s (rounded to two decimal places)
We have the velocity of the second car in m/s. To convert it to km/h, we multiply by 3.6:
8.38 m/s * 3.6 = 30.17 km/h (rounded to two decimal places)
Therefore, the velocity of the second car is approximately 30.17 km/h in the same direction as the compact car.