# Blocks in a room which is being accelerated

• Like Tony Stark
In summary, the equations for ##m_2## with respect to the room are ##x) T-Fr_1-f_1 *=0## and ##y) N_1-P_1=0##, while for ##m_1## they are ##x) N_2=f_2 *## and ##y) T+Fr_2 -P_2=0##. After solving for ##\mu##, the value is found to be ##\mu=0.6##. However, there were some discrepancies in the sign of friction forces and the unconventional choice of the vertical direction for x, leading to a different answer.
Like Tony Stark
Homework Statement
The two bodies shown in the picture have the same mass and are inside a room which is accelerating to the right with ##2 \frac{m}{s^2}##. The coefficient of static friction is the same for both bodies. Determine the minimum value of the coefficient of static friction such that the blocks don't slide with respect to the room and the tension.
Relevant Equations
Newton's equations
I wrote the equations for ##m_2## with respect to the room, which are:
##x) T-Fr_1-f_1 *=0##
##y) N_1-P_1=0##

For ##m_1## we hace:
##x) N_2=f_2 *##
##y) T+Fr_2 -P_2=0##

Where ##f*_1## and ##f*_2## are the pseudo-forces and ##Fr_1## and ##Fr_2## are the friction forces that contain ##\mu##

Then I solved for ##\mu## and got ##\mu =0.6##

Are my ideas correct? Because I wasn't sure about the sign of the friction.

#### Attachments

• 20191004_195022.jpg
59.1 KB · Views: 188
x is in vertical direction? An unconventional choice.
You could have shown the intermediate steps. I get a different answer.

Working purely in the single degree of freedom: m*g is a force towards "m2 goes down", m*a is a force against it (where a=2 m/s^(2)), m*g*μ is against it (friction from m1), m*a*μ is against it (friction from m2).
m(g-a) = mμ(g+a), μ = 8/12 = 2/3.

Like Tony Stark

## What is the relationship between the acceleration of the room and the movement of the blocks?

The acceleration of the room will directly affect the movement of the blocks. As the room accelerates, the blocks will also accelerate in the same direction at the same rate.

## How does the mass of the blocks impact their movement in an accelerated room?

The mass of the blocks will affect the amount of force needed to accelerate them. Objects with larger masses will require more force to accelerate them compared to objects with smaller masses.

## What is the role of friction in an accelerated room with blocks?

Friction can play a significant role in the movement of blocks in an accelerated room. If there is enough friction between the blocks and the surface they are on, it can cause the blocks to stay in place while the room accelerates.

## Will the blocks move in a straight line or a curved path in an accelerated room?

The blocks will move in a straight line in an accelerated room if there is no external force acting on them. However, if there is a force such as friction or air resistance, the blocks may move in a curved path due to the combined effect of the acceleration and the external force.

## How does the direction of acceleration of the room affect the movement of the blocks?

The direction of acceleration of the room will determine the direction in which the blocks will move. If the room is accelerating horizontally, the blocks will also move horizontally. If the room is accelerating vertically, the blocks will move vertically as well.

Replies
18
Views
581
Replies
11
Views
1K
Replies
2
Views
2K
Replies
13
Views
1K
Replies
3
Views
5K
Replies
15
Views
1K
Replies
13
Views
2K
Replies
10
Views
1K
Replies
11
Views
4K
Replies
8
Views
2K