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 answer these questions, we need to use the formula for momentum:
Momentum (p) = mass (m) * velocity (v)
(a) To find the magnitude and direction of the momentum of the compact car, we first need to convert the velocity from kilometers per hour to meters per second. This can be achieved by using the conversion factor 1 km/h = 0.2778 m/s.
Given:
Mass of the compact car (m1) = 705 kg
Velocity of the compact car (v1) = 102 km/h
Converting the velocity:
v1 = 102 km/h * 0.2778 m/s
v1 ≈ 28.28 m/s
Now we can calculate the momentum using the formula:
p1 = m1 * v1
p1 = 705 kg * 28.28 m/s
p1 ≈ 19,938.9 kg·m/s
To represent the momentum on the sketch, draw an arrow pointing to the right (east) with a length of approximately 19,938.9 units (you may use any suitable units).
(b) Now we need to find the velocity of the second car, which has the same momentum as the compact car. Let's assume the mass of the second car is represented by m2, and its velocity is v2.
Using the given information that both cars have the same momentum:
p1 = p2
m1 * v1 = m2 * v2
Given:
Mass of the second car (m2) = 2385 kg
Momentum of the first car (p1) ≈ 19,938.9 kg·m/s
Rearranging the equation to solve for v2:
v2 = (m1 * v1) / m2
v2 = (705 kg * 28.28 m/s) / 2385 kg
v2 ≈ 8.34 m/s
To convert the velocity from meters per second to kilometers per hour, use the conversion factor 1 m/s = 3.6 km/h:
v2 = 8.34 m/s * 3.6 km/h
v2 ≈ 30.02 km/h
Therefore, the velocity of the second car, with the same momentum as the compact car, is approximately 30.02 km/h in the same direction (east).