How Do You Solve a Friction and Motion Problem Involving a Mug and a Tablecloth?

[Zynoakib]

Homework Statement

Q69

Homework Equations

F=ma
v = u + at
v^2 = u^2 + 2as
s = ut + (1/2)at^2

The Attempt at a Solution

Find the deceleration by friction:
F = ma
0.1 = (0.2)a
a = 0.5 ms^-2

and the acceleration of the mug would be 3 - 0.5 = 2.5 ms^-2

Find the time required for the tablecloth to travel 30 cm
u = 0, , s = 0.3, a = 3, t = ?
s = ut + (1/2)at^2
0.3 = (1/2)(3)(t^2)
t = 0.447 s

Find the displacement of mug within 0.447s
t = 0.447, s = ?, u = 0, a = 2.5
s = ut + (1/2)at^2
s = (1/2)(2.5)(0.2)
s= 0.25 m , but the answer is 0.06 m

Thanks!

 

[jbriggs444]

Find the deceleration by friction:
F = ma
0.1 = (0.2)a
a = 0.5 ms^-2

and the acceleration of the mug would be 3 - 0.5 = 2.5 ms^-2

In which direction is the mug accelerating? In which direction does friction between mug and tablecloth act? And what, exactly, do you mean by "a" here?

 

[Qwertywerty]

Find the displacement of mug within 0.447s
t = 0.447, s = ?, u = 0, a = 2.5
s = ut + (1/2)at^2
s = (1/2)(2.5)(0.2)
s= 0.25 m , but the answer is 0.06 m

Thanks!

Is the acceleration of block 2.5m/s^-2 in ground frame ?

Hope this helps .

 

[jbriggs444]

Is the acceleration of block 2.5m/s∧^-2 in ground frame ?

If you draw a free body diagram for the block, what forces act on it?

 

[Qwertywerty]

and the acceleration of the mug would be 3 - 0.5 = 2.5 ms^-2

2.5m/s^-2 is acceleration of block relative to cloth .

 

[jbriggs444]

2.5m/s^-2 is acceleration of block relative to cloth .

Good. And its acceleration relative to the ground is?

 

[Qwertywerty]

Good. And its acceleration relative to the ground is?

0.5m/s^-2 - Thanks jbriggs444 .

 

[Zynoakib]

why is the acceleration of the mug relative to the ground not (2.5 + 3) because the acceleration of the tablecloth is 3 and the mug is sitting on it and accelerate with 2.5 ms^2, so the acceleration of the mug relative to the ground should be 5.5 ms^2

but even if I use a = 0.5 to calculate, I still cannot get the answer. Why's that?

 

[Qwertywerty]

Okay - you seem to be confused .

Try answering these questions :

If you draw a free body diagram for the block, what forces act on it?

then

Acceleration of block relative to cloth is ?

and then

And its acceleration relative to the ground is?

 

[Qwertywerty]

but even if I use a = 0.5 to calculate, I still cannot get the answer. Why's that?

Use a = 0.5m/s² only in your last step - you will get your answer .

Find the displacement of mug within 0.447s
t = 0.447, s = ?, u = 0, a = 2.5
s = ut + (1/2)at^2
s = (1/2)(2.5)(0.2)
s= 0.25 m , but the answer is 0.06 m

Thanks!

 

[Zynoakib]

Thanks, I have got the answer!

But if I want to make the calculation process easier (without the free body diagram), can I just think it in this way?
Since the friction between the mug and the tablecloth is 0.1N, meaning that the force transferred from the tablecloth to the mug for the mug to move can only be 0.1N, so I should

F = ma
0.1 = 0.2a
a = 0.5 ms^-2

 

[Qwertywerty]

But if I want to make the calculation process easier (without the free body diagram), can I just think it in this way?
Since the friction between the mug and the tablecloth is 0.1N, meaning that the force transferred from the tablecloth to the mug for the mug to move can only be 0.1N, so I should

F = ma
0.1 = 0.2a
a = 0.5 ms^-2

Force is not transferred , it is exerted . And no , you don't need the FBD for this question - it was only for you to visualize a bit better .

The rest is fine .

 

[Hercules]

Your working is wrong.
The correct solution is:
mass of mug = 200g = 0.2kg
mug located = 30cm = 0.3m (from the edge of the table)
Acceleration of cloth = 3m/s^2
Using s = ut + 1/2at^2
Finding time:
0.3 = 0+1/2*3*t^2
t = 0.2 sec

Finding the how far mug can move.
s = ut + 1/2at^2
s = 0 + 1/2x3x(0.2)^2
s = 0.06m

The answer is 0.06m.

 

[Qwertywerty]

Using s = ut + 1/2at^2
Finding time:
0.3 = 0+1/2*3*t^2
t = 0.2 sec

You've made a mistake here - t² = 0.2 sec .

Also , try to not solve the entire question - You can read about this in the guidelines .

 

[haruspex]

Your working is wrong.
The correct solution is:
mass of mug = 200g = 0.2kg
mug located = 30cm = 0.3m (from the edge of the table)
Acceleration of cloth = 3m/s^2
Using s = ut + 1/2at^2
Finding time:
0.3 = 0+1/2*3*t^2
t = 0.2 sec

Finding the how far mug can move.
s = ut + 1/2at^2
s = 0 + 1/2x3x(0.2)^2
s = 0.06m

The answer is 0.06m.

That's completely wrong.
First, the given distance is not to the edge of the table, it's to the edge of cloth.
Second, your calculation of the time would find how long it takes for the cloth to move .3m. This does not tell you where the mug is in relation to the cloth at that time.
Third, you then used the acceleration of the cloth as though it were the acceleration of the mug. The only reason you did not end up with an answer of 0.3m is your fourth error, confusing t with t², as Qwertywerty noted.

Fwiw, the quickest way is to note that the acceleration of the mug is 1/6 that of the cloth. Since t² is the same for both, it travels 1/6 of the distance. The difference between the two distances is 0.3m.