Newton's 2nd Law Question PHYCS110

In summary, to find the magnitude of the force exerted by the locomotive on the caboose, we use the equation F = ma and consider the net forces acting on the caboose in the direction of acceleration. Using the given values, we find that the force exerted by the locomotive is 3.5 N.
  • #1
NanoTech
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Hey everyone~

A 2.0 kg toy locomotive is pulling a 1.0 kg caboose. The frictional force of the track on the caboose is 0.50 N backward along the track. Of the train is accelerating foward at 3.0 m/s^2, what is the magnitude of the force exerted by the locomotive on the caboose?

So I'm guessing that I use the equation: F = ma, but I'm not sure how to get started. The answer in the back of the book is: 3.5 N. Thanks for your input~David.W
 
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  • #2
NanoTech said:
Hey everyone~

A 2.0 kg toy locomotive is pulling a 1.0 kg caboose. The frictional force of the track on the caboose is 0.50 N backward along the track. Of the train is accelerating foward at 3.0 m/s^2, what is the magnitude of the force exerted by the locomotive on the caboose?

So I'm guessing that I use the equation: F = ma, but I'm not sure how to get started. The answer in the back of the book is: 3.5 N. Thanks for your input~David.W
[tex]F_{net}\ =\ ma[/tex]

Now, you know the mass. Also, you know the acceleration of the train, so it should be pretty obvious as to what the acceleration of the caboose is. (Think about it, if my body is accelerating at X, then what would be the acceleration of my head, arm, finger... ?) So, you should be able to find the net force on the train. Since the train is accelerating parallel to the ground, find the net forces acting on the caboose in the direction parallel to the ground. What are these forces? Figure them out, and set up an equation to find the force exerted by the engine on the caboose.
 
  • #3


Hi David,

You're on the right track! To find the magnitude of the force exerted by the locomotive on the caboose, we can use Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F=ma).

In this scenario, the net force acting on the caboose is the force exerted by the locomotive (forward) minus the frictional force of the track (backward). So we can set up the equation as:

F - 0.50 N = (1.0 kg)(3.0 m/s^2)

We can rearrange this equation to solve for F:

F = (1.0 kg)(3.0 m/s^2) + 0.50 N

F = 3.0 N + 0.50 N

F = 3.50 N

So the magnitude of the force exerted by the locomotive on the caboose is 3.50 N, which is consistent with the answer in the back of the book.

Hope this helps! Let me know if you have any other questions or need clarification. Happy studying!
 

FAQ: Newton's 2nd Law Question PHYCS110

What is Newton's 2nd Law of Motion?

Newton's 2nd Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that the greater the force applied to an object, the greater its acceleration will be. Similarly, the larger the mass of an object, the smaller its acceleration will be.

How is Newton's 2nd Law mathematically represented?

Newton's 2nd Law can be mathematically represented as F=ma, where F is the net force, m is the mass of the object, and a is the acceleration. This formula shows that the force and acceleration are directly proportional, while the mass and acceleration are inversely proportional.

What are some real-life examples of Newton's 2nd Law?

Some common examples of Newton's 2nd Law in action include pushing a shopping cart, throwing a ball, and riding a bike. In each of these scenarios, the force applied to the object (shopping cart, ball, bike) results in an acceleration of the object in the same direction as the force.

How does Newton's 2nd Law relate to inertia?

Newton's 2nd Law is closely related to the concept of inertia, which is an object's resistance to change in its motion. According to Newton's 2nd Law, an object with a larger mass will have a greater inertia, meaning it will require a larger force to accelerate it compared to an object with a smaller mass.

Can Newton's 2nd Law be applied to non-uniform or changing forces?

Yes, Newton's 2nd Law can be applied to non-uniform or changing forces by using calculus. In these cases, the force is divided into small increments and the acceleration is calculated for each increment. These accelerations are then added together to determine the overall acceleration of the object.

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