Solving for a Train Without Knowing Mass

In summary, the train is traveling up a 3.73 degree incline at 3.25 m/s and the last car breaks free and begins to coast without friction. Using Newton's second law, the mass of the train is not needed to determine how long it will take for the last car to come to rest momentarily or how far the last car traveled before coming to rest.
  • #1
kmm0830
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A train is traveling up a 3.73 degree incline at 3.25 m/s when the last car breaks free and begins to coast without friction. A) How long does it take for the last car to come to rest momentarily? B) How far did the last car travel before coming to rest?



Newtons Second Law



I know that you must use Newton's second law here, but do not understand how to solve this problem without knowing the mass of the train to determine how long it will take for it to stop.
 
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welcome to pf!

hi kmm0830! welcome to pf! :smile:
kmm0830 said:
I know that you must use Newton's second law here, but do not understand how to solve this problem without knowing the mass of the train to determine how long it will take for it to stop.

standard trick …

call the mass "m", and carry on anyway …

you'll find that m will cancel out at the end! :wink:​
 

What are Newton's Laws and how do they apply to a train?

Newton's Laws are three fundamental principles of physics that describe the motion of objects. They apply to all types of motion, including that of a train. The first law states that an object will remain at rest or in uniform motion unless acted upon by an external force. The second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction.

How does Newton's first law apply to a moving train?

In the case of a moving train, Newton's first law explains why the train keeps moving at a constant speed unless acted upon by an external force, such as friction from the tracks or air resistance. It also explains why passengers inside the train continue to move at the same speed and direction as the train, even when it turns or stops suddenly.

How does Newton's second law apply to a train?

Newton's second law explains the relationship between the net force on an object, its mass, and its acceleration. In the case of a train, the net force is the sum of all the forces acting on the train, such as the force of the engine, air resistance, and friction. The mass of the train will determine how much acceleration is produced by a given net force.

How does Newton's third law apply to a train?

Newton's third law explains the equal and opposite nature of forces. In the case of a train, this means that when the train moves forward, it exerts an equal force in the opposite direction on the tracks. This force allows the train to move forward by pushing against the tracks. Similarly, when the train stops, the force of the brakes on the tracks is equal and opposite to the force of the train's motion, causing it to come to a halt.

What role do Newton's Laws play in designing and operating trains?

Newton's Laws are essential in designing and operating trains. Engineers use these laws to calculate the forces acting on the train and determine the best design for efficiency and safety. Train operators also use these laws to understand the train's motion and how to control it effectively. Without an understanding of Newton's Laws, trains would not be able to function as efficiently and safely as they do today.

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