M1 Motion with friction Watch

indigorain
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Hi! I was wondering if anyone could help me with this question and guide me through the steps? Thanks!

A body is sliding along a smooth horizontal surface at a constant speed of 5m/s. It moves onto a rough horizontal surface where the coefficient of friction is 0.5. Find the distance the body will travel across this surface before coming to rest.

The answer my book gives is 2.55m.

Thanks!
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davros
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(Original post by indigorain)
Hi! I was wondering if anyone could help me with this question and guide me through the steps? Thanks!

A body is sliding along a smooth horizontal surface at a constant speed of 5m/s. It moves onto a rough horizontal surface where the coefficient of friction is 0.5. Find the distance the body will travel across this surface before coming to rest.

The answer my book gives is 2.55m.

Thanks!
This is just standard SUVAT!

Do you know what force, and hence what acceleration, acts on the body?

Can you work out which SUVAT equation you need to use?
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Jordan97
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(Original post by davros)
This is just standard SUVAT!

Do you know what force, and hence what acceleration, acts on the body?

Can you work out which SUVAT equation you need to use?
There's a little bit more to it than just SUVAT. You first need to work out the magnitude of the frictional force and hence the deceleration it causes first.

Also is this the full question? I'm pretty sure you'd need to know the mass of the box to do anything with it
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davros
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(Original post by Jordan97)
There's a little bit more to it than just SUVAT. You first need to work out the magnitude of the frictional force and hence the deceleration it causes first.

Also is this the full question? I'm pretty sure you'd need to know the mass of the box to do anything with it
I was trying to prompt the OP to see how far they'd got with thinking about the problem

And you don't need the mass - I wondered about the question myself, so I tried it out and the mass cancels out when you work out the deceleration!
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indigorain
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(Original post by davros)
I was trying to prompt the OP to see how far they'd got with thinking about the problem

And you don't need the mass - I wondered about the question myself, so I tried it out and the mass cancels out when you work out the deceleration!
I think I've managed to figure it out - thanks for your help!

That said, is this the method you would use?

Initial speed when it hits the rough plane is 5m/s

Frictional force = 0.5mg = 4.9m

Frictional force = ma (this is the step I'm a bit confused about - is it in equilibrium? If so, why is it decelerating?)

a = F/m

a = 0.5mg / m

a = 0.5g = 4.9 m/s^2

Then use UVAST to get s = 2.55m
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davros
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(Original post by indigorain)
I think I've managed to figure it out - thanks for your help!

That said, is this the method you would use?

Initial speed when it hits the rough plane is 5m/s

Frictional force = 0.5mg = 4.9m

Frictional force = ma (this is the step I'm a bit confused about - is it in equilibrium? If so, why is it decelerating?)

a = F/m

a = 0.5mg / m

a = 0.5g = 4.9 m/s^2

Then use UVAST to get s = 2.55m
It's not "in equilibrium" because it's moving!

Friction is the only resistive force, and because the body is moving, friction is limiting so you can use F = 0.5R = 0.5mg.

So the acceleration (or deceleration if you prefer) is a = F/m = 0.5g as you've written.

And now you just need to use SUVAT with u = 5, v = 0 to get s.
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indigorain
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(Original post by davros)
It's not "in equilibrium" because it's moving!

Friction is the only resistive force, and because the body is moving, friction is limiting so you can use F = 0.5R = 0.5mg.

So the acceleration (or deceleration if you prefer) is a = F/m = 0.5g as you've written.

And now you just need to use SUVAT with u = 5, v = 0 to get s.
Great, thank you very much!
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