# Law of motion problem

## 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!

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jbriggs444
Homework Helper
2019 Award
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?

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
Homework Helper
2019 Award
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?

• Zynoakib
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
Homework Helper
2019 Award
2.5m/s-2 is acceleration of block relative to cloth .
Good. And its acceleration relative to the ground is?

• Zynoakib
Good. And its acceleration relative to the ground is?
0.5m/s-2 - Thanks jbriggs444 .

Last edited:
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?

Last edited:
Okay - you seem to be confused .

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?

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

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

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 .

Last edited:
• Zynoakib
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

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 .

haruspex
Homework Helper
Gold Member
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