Mechanics deceleration question

Original post by Sidd1

I always get confused when the term deceleration is used in questions... does it mean when something slows down ? Will it change direction as a result or no? For example:

The train must stop at the next station so the driver reduces the force produced by the engine to 0 and applies the brakes. The brakes produce a force on the train of magnitude 2000N causing engine and carriage to decelerate. Give that the resistances to motion are unchanged, find the magnitude of the thrust in the shunt. mechanics q 2.png

Why is the direction to the left now? Is it due to deceleration??

Deceleration means that the velocity is decreasing. Therefore the direction of the acceleration is opposite to that of the velocity. Since F=ma there must be a resultant force in the opposite direction to the velocity.

Reply 2

RogerOxon

Original post by Sidd1

I always get confused when the term deceleration is used in questions... does it mean when something slows down ? Will it change direction as a result or no? For example:

The train must stop at the next station so the driver reduces the force produced by the engine to 0 and applies the brakes. The brakes produce a force on the train of magnitude 2000N causing engine and carriage to decelerate. Give that the resistances to motion are unchanged, find the magnitude of the thrust in the shunt. mechanics q 2.png

Why is the direction to the left now? Is it due to deceleration??

Original post by David Getling

Deceleration means that the velocity is decreasing. Therefore the direction of the acceleration is opposite to that of the velocity. Since F=ma there must be a resultant force in the opposite direction to the velocity.

Warning: I'm going to be pedantic. Be aware that the term "velocity" is widely misused.

Velocity is a vector, so it cannot be "decreasing". It's magnitude can never be negative.

Speed is a scalar, (typically) with a particular direction defined as positive. Decelerating means that the speed along that direction is decreasing, and may become negative.

As example, consider a car coasting up an incline. It's speed (defined as positive up the incline) will reduce, and, assuming that it doesn't make the top, become negative. The magnitude of its velocity will initially reduce, to zero, then increase again.

In the question that you quoted, we say that the train is decelerating because its speed in the the direction of (initial) travel is decreasing.

(edited 4 years ago)

Reply 3

Original post by RogerOxon

Velocity is a vector, so it cannot be "decreasing".

Rubbish! Of course a vector can decrease in size.

Reply 4

RogerOxon

Original post by David Getling

Rubbish! Of course a vector can decrease in size.

Its magnitude can decrease, but "it" cannot.

Reply 5

Original post by RogerOxon

Its magnitude can decrease, but "it" cannot.

You're splitting hairs. If the direction doesn't change I think you will find most mathematicians wouldn't make such a fine distinction.

Reply 6

Sidd1

OP

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Original post by David Getling

Deceleration means that the velocity is decreasing. Therefore the direction of the acceleration is opposite to that of the velocity. Since F=ma there must be a resultant force in the opposite direction to the velocity.

I was talking about part c of this question - this was the "decelrating" part that confused me. I couldn't get why they sai the positive direction is to the left now when they do F = ma

Reply 7

Original post by Sidd1

I always get confused when the term deceleration is used in questions... does it mean when something slows down ? Will it change direction as a result or no? For example:

The train must stop at the next station so the driver reduces the force produced by the engine to 0 and applies the brakes. The brakes produce a force on the train of magnitude 2000N causing engine and carriage to decelerate. Give that the resistances to motion are unchanged, find the magnitude of the thrust in the shunt. mechanics q 2.png

Why is the direction to the left now? Is it due to deceleration??

Just think of it in real life : if you're in a vehicle that is travelling at some velocity and the breaks are applied, the vehicle will start to slow down but it won't instantaneously change direction. It slows down because the force acting on it (by the breaks) is in the opposite direction to motion - this is what deceleration is.

In the diagram, the force due to the breaking force is pointing to the left so the acceleration is also pointing to the left. But the train is still moving to the right until it stops moving. Make sense?

(edited 4 years ago)

Reply 8

Sidd1

OP

13

Original post by Sir Cumference

Just think of it in real life : if you're in a vehicle that is travelling at some velocity and the breaks are applied, the vehicle will start to slow down but it won't instantaneously change direction. It slows down because the force acting on it (by the breaks) is in the opposite direction to motion - this is what deceleration is.

In the diagram, the force due to the breaking force is pointing to the left so the acceleration is also pointing to the left. But the train is still moving to the right until it stops moving. Make sense?

Okay that makes so much sense thank you :smile:

so does acceleration and the force act oppositely to the direction of motion?

Reply 9

Original post by Sidd1

Okay that makes so much sense thank you :smile:

so does acceleration and the force act oppositely to the direction of motion?

In this case yes and this is what causes the train to slow down.

Reply 10

Original post by David Getling

You're splitting hairs. If the direction doesn't change I think you will find most mathematicians wouldn't make such a fine distinction.

I disagree. At this level I think it's important to be careful with terminology otherwise students could get confused, and they often are by this topic.

"Deceleration means that the velocity is decreasing."

If the velocity of a particle changes from 20 to 10 then using the above you would say that the velocity is "decreasing" and this is deceleration. If the velocity continues to "decrease" and becomes negative then the particle is now accelerating because the speed is increasing.

"Deceleration means that the speed is decreasing."

The above is more correct and won't cause confusion.

(edited 4 years ago)

Reply 11

RogerOxon

Original post by David Getling

You're splitting hairs. If the direction doesn't change I think you will find most mathematicians wouldn't make such a fine distinction.

How many Mathematicians do you know? These are the people that think that you need to prove that 1+1=2.

Reply 12

Original post by RogerOxon

How many Mathematicians do you know? These are the people that think that you need to prove that 1+1=2.

It may surprise you to know that I am aware of the work that people like Russell and Whitehead did on stuff like this :smile:

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Reply 13

Original post by Sir Cumference

I disagree. At this level I think it's important to be careful with terminology otherwise students could get confused, and they often are by this topic.

"Deceleration means that the velocity is decreasing."

If the velocity of a particle changes from 20 to 10 then using the above you would say that the velocity is "decreasing" and this is deceleration. If the velocity continues to "decrease" and becomes negative then the particle is now accelerating because the speed is increasing.

"Deceleration means that the speed is decreasing."

The above is more correct and won't cause confusion.

Whatever the rights and wrongs, you haven't argued the case well. Can you really not see that what you have said in the third paragraph applies equally to your favoured definition. So we have parity of confusion :smile:

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Reply 14

Original post by David Getling

Whatever the rights and wrongs, you haven't argued the case well. Can you really not see that what you have said in the third paragraph applies equally to your favoured definition. So we have parity of confusion :smile:

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I don't know what you mean - can you explain further? If the velocity decreases from -20 to -30 then the speed has increased and so there is no deceleration.

Reply 15

Original post by Sir Cumference

I don't know what you mean - can you explain further? If the velocity decreases from -20 to -30 then the speed has increased and so there is no deceleration.

By your own earlier argument, if the speed continues to decrease it will eventually reach 0 and then start to increase, so deceleration becomes acceleration.

I think you might be implying that what I said is different from this, but it's exactly the same. Unless (like a lawyer) you have decided to only consider my first sentence and ignore the other two.

Reply 16