A pair of fuzzy dice hang from the rear view mirror of a car. For each of the motions indicate which way the dice would move and why:
a) constant velocity forward
b) speeding up backward
c) slowing down forward
I understand that when the car's state of motion changes, in the split seconds after the change, the objects in the car are still responding to inertia so they hold on to their previous state of motion.
I am wondering, do the objects in the car always catch up to the car's state of motion eventually because they are attached to the car and are also experiencing the forces indirectly?
When the car accelerates forward. the dice retain their old slower speed instantaneously and fall back. However then the tension in the string they are hanging by has a forward component of force on the dice because of its angle. That accelerates the dice forward with the car and the dice remain at that angle back from vertical until the car resumes constant speed again. At that point the dice are no longer needing a forward force to accelerate with the car and the string resumes its vertical hang angle.
In general, objects inside a car will eventually catch up to the car's state of motion because they are indirectly experiencing the forces acting on the car. Let's analyze the specific scenarios you mentioned:
a) Constant velocity forward: In this case, the car is moving forward at a constant speed. The fuzzy dice, being attached to the car, will also move forward at the same velocity as the car. Thus, the dice will remain stationary relative to the car and hang straight down.
b) Speeding up backward: If the car starts speeding up in the backward direction, the dice will initially resist this change in motion due to their inertia. As a result, they will appear to move backward relative to the car. However, since the dice are attached to the car, they will gradually catch up with the increasing backward velocity and eventually hang straight down again.
c) Slowing down forward: If the car starts slowing down while moving forward, the dice will initially resist the change in motion due to their inertia. As a result, they will appear to move forward relative to the car. However, as the car continues to decelerate, the backward force acting on the dice will decrease. Eventually, the dice will catch up to the car's decreasing forward velocity and hang straight down again.
In both cases of speeding up backward and slowing down forward, the objects inside the car will experience a temporary shift in their state of motion relative to the car due to inertia. However, because they are attached to the car, they will eventually catch up and adapt to the car's new state of motion.
To determine which way the fuzzy dice would move in each scenario, we need to consider the concept of inertia.
First, remember that inertia is the tendency of an object to resist changes in its state of motion. When the car's state of motion changes, the objects inside the car will initially continue to have their previous state of motion due to inertia.
Now let's analyze each scenario:
a) Constant velocity forward: In this case, the car is maintaining a steady speed in the forward direction. The fuzzy dice hanging from the rearview mirror will also continue to move forward at a constant velocity. This is because, due to inertia, the dice will resist changes in their state of motion and will move with the car.
b) Speeding up backward: If the car suddenly starts accelerating in the backward direction, the fuzzy dice will initially tend to resist this change and continue moving forward. However, since the dice are attached to the car and are indirectly experiencing the acceleration forces, they will eventually start moving backward to catch up with the car's new state of motion.
c) Slowing down forward: When the car starts decelerating or slowing down in the forward direction, the fuzzy dice will initially continue moving forward due to inertia. However, since the dice are indirectly experiencing the deceleration forces through their attachment to the car, they will eventually slow down and catch up with the car's new state of motion.
In summary, while objects in the car initially hold on to their previous state of motion due to inertia, they will eventually adjust and catch up to the car's new state of motion because they are attached to the car and indirectly experience the forces acting on it.