Q2. A box rests on the (frictionless) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground next to the truck, and (b) by Chris who is riding on the truck.
A) can be explained by Newton's 1st law.
B) can be explained by Newton's third?
I will be happy to critique your thinking. Start with f=ma, and newtons first law.
(a) As seen by Mary standing on the ground next to the truck:
According to Newton's First Law (the law of inertia), an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. Therefore, when the truck starts accelerating forward, the box will tend to stay at rest due to its inertia. However, there is an external force acting on the box, namely the friction between the box and the truck bed.
As the truck accelerates forward, the box will experience a backward force of friction. This force is what causes the box to start sliding toward the rear of the truck. Eventually, the force of friction will be enough to overcome the inertia of the box, and it will move with the same acceleration as the truck.
(b) As seen by Chris who is riding on the truck:
Chris is in an accelerating reference frame, so they need to consider the apparent forces acting on the box. From Chris' point of view, the box appears to be at rest since the truck and the box are both accelerating forward at the same rate.
According to Newton's Second Law (F = ma), the box will experience an apparent forward force equal to the mass of the box multiplied by the acceleration of the truck. This force is what keeps the box seemingly stationary relative to Chris.
However, it is important to note that Chris is observing this apparent equilibrium because they are also in the accelerating frame of reference. In reality, from an external observer's perspective, the box is indeed moving backward relative to the truck bed due to the force of friction.
To understand the motion of the box in this scenario, let's analyze it from two different perspectives:
(a) Mary standing on the ground next to the truck:
According to Newton's first law of motion (the law of inertia), an object at rest tends to stay at rest unless acted upon by an external force. Thus, when the truck starts moving, the box tends to remain at rest due to its inertia. However, a frictional force arises between the box and the truck bed due to the interaction between their surfaces.
If the truck accelerates forward, the box experiences an external force in the opposite direction (towards the rear). As a result, the box overcomes its inertia and slides towards the rear of the truck. The frictional force between the box and the truck bed is responsible for this motion. Therefore, from Mary's perspective, the box appears to be sliding towards the rear of the truck.
(b) Chris riding on the truck:
As Chris is riding on the truck, he moves along with it, maintaining the same acceleration. According to the principle of relativity, Chris and the box are in the same frame of reference as they are both on the truck.
From Chris's perspective, the box may be at rest or appears to move forward, similar to the motion of the truck itself. This is because Chris experiences the same acceleration as the truck and is effectively moving along with it. Thus, the box does not appear to slide towards the rear of the truck from Chris's perspective.
In both cases, the motion of the box can be explained using Newton's laws of motion. The difference in perception arises due to the different frames of reference (Mary standing on the ground and Chris riding on the truck) from which the observation is made.