Maths question help please

13

Hi, please could I have help on this question. I’m unsure which acceleration to use for when it is smooth and when it is rough.
Question: https://ibb.co/svbK7Y1K
Thank you!

Reply 1

mqb2766

21

Original post

by anonymous56754

Hi, please could I have help on this question. I’m unsure which acceleration to use for when it is smooth and when it is rough.
Question: https://ibb.co/svbK7Y1K
Thank you!

Sounds like its 0.9m/s^2 for the first part, then the motion is smooth (gravity) for the second part?

Reply 2

anonymous56754

OP

13

Original post

by mqb2766

Sounds like its 0.9m/s^2 for the first part, then the motion is smooth (gravity) for the second part?

Why is it 0.9 for the first part, how can you tell? Also for the second part a=gsin 30, again I’m not really sure why

Reply 3

mqb2766

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Original post

by anonymous56754

Why is it 0.9 for the first part, how can you tell? Also for the second part a=gsin 30, again I’m not really sure why

The question states the 0.9m/s^2 for the first part.
For the second part, resolve gravity down the slope as P is moving down a smooth slope at 30 degrees.

Reply 4

anonymous56754

OP

13

Original post

by mqb2766

The question states the 0.9m/s^2 for the first part.
For the second part, resolve gravity down the slope as P is moving down a smooth slope at 30 degrees.

thank you, but how do we know it is 0.9 for the rough part and not the smooth part?

Reply 5

mqb2766

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Original post

by anonymous56754

thank you, but how do we know it is 0.9 for the rough part and not the smooth part?

The question says you have two objects which are joined by a taut string. The lower one wants to accelerate at resolved gravity as that part of the slope is smooth, but the upper one is travelling on a rough surface which re tards motion. The string remains taut (so you have a single body) and both objects are accelerating at 0.9 m/s^2 down the slope as the question says.

Reply 6

anonymous56754

OP

13

Original post

by mqb2766

The question says you have two objects which are joined by a taut string. The lower one wants to accelerate at resolved gravity as that part of the slope is smooth, but the upper one is travelling on a rough surface which re tards motion. The string remains taut (so you have a single body) and both objects are accelerating at 0.9 m/s^2 down the slope as the question says.

Oh ok, so if it is a smooth surface it will always travel at g or resolved g but if it is a rough surface, it will travel at the acceleration stated?

Reply 7

mqb2766

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Original post

by anonymous56754

Oh ok, so if it is a smooth surface it will always travel at g or resolved g but if it is a rough surface, it will travel at the acceleration stated?

For this example (travelling down an inclined plane) when the surface is smooth, there will be the usual (resolved) gravitational force acting on the body, but if its rough, theres also a re tarding force to consider. So the resultant force acting on the body
resolved gravitational - friction
is less than just the resolved gravitational force. This keeps the string taut (first part) and the question tells you what the acceleration of both masses/the combined system (as the string is taut) is. The tension in the string "averages" out the individual forces/accelerations on the individual bodies.

If youre unsure, you should really sketch a force diagram and do some simple thought experiments to make sure you set up the problem correctly.

Reply 8

anonymous56754

OP

13

Original post

by mqb2766

For this example (travelling down an inclined plane) when the surface is smooth, there will be the usual (resolved) gravitational force acting on the body, but if its rough, theres also a re tarding force to consider. So the resultant force acting on the body
resolved gravitational - friction
is less than just the resolved gravitational force. This keeps the string taut (first part) and the question tells you what the acceleration of both masses/the combined system (as the string is taut) is. The tension in the string "averages" out the individual forces/accelerations on the individual bodies.
If youre unsure, you should really sketch a force diagram and do some simple thought experiments to make sure you set up the problem correctly.

Oh ok so I understand that the acceleration on a rough surface depends on the resultant force due to resolved gravity- friction but I don’t really understand its link to the string being taut? What does the string being taut mean? Thank you

Reply 9

mqb2766

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Original post

by anonymous56754

Oh ok so I understand that the acceleration on a rough surface depends on the resultant force due to resolved gravity- friction but I don’t really understand its link to the string being taut? What does the string being taut mean? Thank you

Im guessing youre in year 13, is that right?

But if the string is slack, the two objects would move independently. So in the second part of the question, the leading mass is stationary at the bottom (velocity, acceleration = 0) whereas the trailing mass on the smooth surface catches it up and the acceleration is given by resolved gravity (non zero velocity down the slope). If it was a spring rather than a string, the spring would enter compression, but its a string and when its slack, masses at each end behave independently.

When the string is taut (first part of the question), the distance between the masses is constant. So they must move with the same velocity and acceleration, somewhat like a car towing a caravan. Here as friction is re tarding the motion of the trailing mass and hence the leading mass through the non zero tension, the string must be taut as the trailing mass wants to move slower than the leading mass (roughly). The taut string ensures they move at the same velocity and acceleration, so it "averages" the effect of the forces on the individual bodies. Hence the suggestion about writing down the force equation(s) and eliminating tension.