A bolt drops from the ceiling of a train car that is accelerating northward at a rate of 3.15 m/s2.

What is the acceleration of the bolt relative to the train car?

I don't understand how to do this problem at all... and why isn't it zero? It seems if the train is going forward and the bolt is going backward at the same acceleration the acceleration should be zero?

acceleration is caused by forces.

After the bolt is released, the only force on it is gravity. Horizontally, acceleration is zero, there is no horizontal force on the bolt. Vertically, gravity is operating on it.

. The problem statement, all variables and given/known data

A bolt drops from the ceiling of a train car that is accelerating northward at a rate of 3.50 m/s2.
(a) What is the acceleration of the bolt relative to the train car?
(b) What is the acceleration of the bolt relative to the Earth?

3. The attempt at a solution
(a)10.4 m/s2 at 19.7° to the south from the vertical
(b)9.8 m/s2 vertically downward


I don't understand why the acceleration in (a) is not vertically downward since it is relative to the train. As we could assume the train is not moving, then the motion should be vertically downward isn't?

To find the acceleration of the bolt relative to the train car, we need to consider the forces acting on the bolt.

While the train is accelerating northward, there are two forces acting on the bolt. The first is the gravitational force pulling the bolt downward, and the second is the normal force exerted by the train car pushing the bolt upward.

In this scenario, the bolt is not attached or connected to the train car. Therefore, it is free to move independently under the influence of gravitational force. As the train accelerates, the bolt will still be subject to the gravitational force, causing it to accelerate downward relative to the train car.

The acceleration of the bolt relative to the train car is the same as its acceleration due to gravity, which is approximately 9.8 m/s^2.

So, the acceleration of the bolt relative to the train car is 9.8 m/s^2 downward.

To determine the acceleration of the bolt relative to the train car, we need to consider the relative motion between the two.

If we assume that the positive direction is in the northern direction, then the acceleration of the train car is given as 3.15 m/s^2 northward. Since the bolt drops straight down from the ceiling, its initial velocity in the north direction is zero.

Now, let's break down the motion of the bolt into horizontal and vertical components:

1. Horizontal Motion:
Since the bolt is dropping straight down, its horizontal velocity remains zero throughout the motion. Therefore, the horizontal acceleration of the bolt relative to the train car is also zero.

2. Vertical Motion:
The bolt experiences a downward acceleration due to gravity. However, this acceleration is unrelated to the acceleration of the train car. The acceleration due to gravity is approximately 9.8 m/s^2 downward, regardless of the horizontal motion.

So, the acceleration of the bolt relative to the train car is the same as the acceleration due to gravity, approximately 9.8 m/s^2 downward. The acceleration due to the train's northward motion does not affect the vertical acceleration of the bolt.