An old Chrysler with mass 1800 kg is moving along a straight stretch of road at 58 km/h. It is followed by a Ford with mass 1400 kg moving at 70 km/h. How fast is the center of mass of the two cars moving?
To calculate the speed of the center of mass of the two cars, we need to use the concept of conservation of momentum.
The momentum of an object is given by the formula p = m * v, where p is the momentum, m is the mass, and v is the velocity.
The total momentum of the two cars is the sum of their individual momenta.
For the old Chrysler:
Mass (m1) = 1800 kg
Velocity (v1) = 58 km/h = 58 * (1000/3600) m/s = 16.111 m/s
Momentum (p1) = m1 * v1
For the Ford:
Mass (m2) = 1400 kg
Velocity (v2) = 70 km/h = 70 * (1000/3600) m/s = 19.444 m/s
Momentum (p2) = m2 * v2
The total momentum of the two cars (p_total) is:
p_total = p1 + p2
To find the speed of the center of mass, we need to divide the total momentum by the total mass of the two cars.
Total mass (m_total) = m1 + m2
Now we can calculate the speed of the center of mass (v_cm):
v_cm = p_total / m_total
Let's calculate it step by step.
First, calculate p1:
p1 = m1 * v1
p1 = 1800 kg * 16.111 m/s
Next, calculate p2:
p2 = m2 * v2
p2 = 1400 kg * 19.444 m/s
Now, calculate p_total:
p_total = p1 + p2
Calculate m_total:
m_total = m1 + m2
Finally, calculate v_cm:
v_cm = p_total / m_total
Plug in the values and calculate the final answer.
To find the speed of the center of mass of the two cars, we need to use the concept of conservation of momentum. The total momentum of an isolated system remains constant unless acted upon by external forces.
The momentum of an object is given by the product of its mass and velocity. Therefore, the momentum of the Chrysler is given by its mass (1800 kg) multiplied by its velocity (58 km/h). Similarly, the momentum of the Ford is given by its mass (1400 kg) multiplied by its velocity (70 km/h).
To find the total momentum, we add the individual momenta of the two cars:
Total momentum = momentum of Chrysler + momentum of Ford
Now, we need to convert the velocities from km/h to m/s since the SI unit of mass is kilograms and the SI unit of velocity is meters per second. To convert km/h to m/s, divide the velocity by 3.6.
So, the momentum of the Chrysler is (1800 kg) * (58 km/h) / (3.6) = 290000 kg·m/s.
The momentum of the Ford is (1400 kg) * (70 km/h) / (3.6) = 272222 kg·m/s.
Adding these momenta, we get the total momentum:
Total momentum = 290000 kg·m/s + 272222 kg·m/s = 562222 kg·m/s.
Now, to find the speed of the center of mass, we divide the total momentum by the total mass of the two cars:
Center of mass speed = total momentum / total mass
The total mass is the sum of the masses of the Chrysler and Ford, i.e., 1800 kg + 1400 kg = 3200 kg.
Therefore, the center of mass speed = 562222 kg·m/s / 3200 kg ≈ 175.70 m/s.
Hence, the center of mass of the two cars is moving at approximately 175.70 m/s.