A 7150-kg railroad car travels alone on a level frictionless track with a constant speed of 15.0 m/s. A 3350-kg load, initially at rest, is dropped onto the car. What will be the car's new speed?
conserve momentum
7150*15.0 = (7150+3350)v
v = 10.21 m/s
Well, we certainly have a "weighty" situation here! When the load is dropped onto the railroad car, we need to take a look at the principle of conservation of momentum.
Since there are no external forces acting on the system, the total momentum before and after the load is dropped onto the car should remain the same. We can express this as:
(mass of car x velocity of car) + (mass of load x velocity of load before) = (mass of car + mass of load) x velocity of system after
Plugging in the given values, we get:
(7150 kg x 15.0 m/s) + (3350 kg x 0 m/s) = (7150 kg + 3350 kg) x velocity of system after
Simplifying:
(107,250 kg·m/s) = (10,500 kg) x velocity of system after
Now, we can solve for the velocity of the system after the load is dropped:
Velocity of system after = 107,250 kg·m/s / 10,500 kg
Velocity of system after ≈ 10.21 m/s
So, after this "weighty" addition, the railroad car's new speed will be approximately 10.21 m/s.
To find the car's new speed after the load is dropped onto it, we can use the principle of conservation of momentum. The total momentum before the load is dropped is equal to the total momentum after the load is dropped.
The momentum of an object is given by the product of its mass and velocity.
Before the load is dropped:
The momentum of the railroad car is calculated as:
momentum_car = mass_car * velocity_car
Given that the mass of the car (m_car) is 7150 kg and the initial velocity (v_car) is 15.0 m/s, we have:
momentum_car = 7150 kg * 15.0 m/s
The momentum of the load is initially at rest, so:
momentum_load = 0 kg * v_load
After the load is dropped:
The total momentum of the system (car + load) is equal to:
momentum_total = (mass_car + mass_load) * velocity_new
Given that the mass of the load (m_load) is 3350 kg and we want to find the new velocity (v_new), we can rewrite the momentum equation as:
momentum_total = (m_car + m_load) * v_new
Since the total momentum before and after the load is dropped should be equal, we have:
momentum_car + momentum_load = momentum_total
The equation becomes:
(m_car * v_car) + (0 kg * v_load) = (m_car + m_load) * v_new
Now we can solve for the new velocity (v_new):
(m_car * v_car) = (m_car + m_load) * v_new
v_new = (m_car * v_car) / (m_car + m_load)
Substituting the given values:
v_new = (7150 kg * 15.0 m/s) / (7150 kg + 3350 kg)
v_new = 107250 kg·m/s / 10500 kg
v_new ≈ 10.22 m/s
Therefore, the car's new speed will be approximately 10.22 m/s after the load is dropped onto it.
To find the car's new speed after the load is dropped onto it, we can use the principle of conservation of momentum.
First, let's calculate the initial momentum of the car before the load is dropped onto it. The momentum (p) of an object can be calculated by multiplying its mass (m) by its velocity (v):
Initial momentum of the car = mass of the car * velocity of the car
= 7150 kg * 15.0 m/s
= 107,250 kg·m/s
Since the load was initially at rest, its initial momentum is zero.
Now, after the load is dropped onto the car, the system will have a total mass of:
mass of the car + mass of the load = 7150 kg + 3350 kg = 10,500 kg
To find the final velocity of the system, we can use the conservation of momentum principle. According to this principle, the total momentum before the event should equal the total momentum after the event:
Initial momentum of the system = Final momentum of the system
Before the event, the initial momentum of the system is the momentum of the car alone (since the load is at rest).
Final momentum of the system = (mass of the system) * (final velocity of the system)
So, we can set up the equation as follows:
Initial momentum of the system = Final momentum of the system
Initial momentum of the car = Final momentum of the system
or
(mass of the car) * (initial velocity of the car) = (mass of the system) * (final velocity of the system)
Plugging in the values we know:
(7150 kg) * (15.0 m/s) = (10,500 kg) * (final velocity of the system)
Simplifying:
107,250 kg·m/s = 10,500 kg * (final velocity of the system)
Now, we can solve for the final velocity of the system (which is the new speed of the car):
(final velocity of the system) = (107,250 kg·m/s) / (10,500 kg)
(final velocity of the system) ≈ 10.2 m/s
Therefore, the car's new speed after the load is dropped onto it will be approximately 10.2 m/s.