# What Is the Least Time for Blocks to Move 7.20m Without Sliding?

• Nbwx
In summary: The maximum horizontal force that can be transmitted to the bottom block via the top block is 16.75 N. The force impedes the bottom block's motion is the coefficient of kinetic friction. You can't draw a FBD for the bottom block including these forces.
Nbwx

## Homework Statement

The coefficient of static friction is 0.673 between the two blocks shown. The coefficient of kinetic friction between the lower block and the floor is 0.113. Force F causes both blocks to cross a distance of 7.20m, starting from rest. What is the least amount of time in which the motion can be completed without the top block sliding on the lower block, if the mass of the lower block is 1.90kg and the mass of the upper block is 2.54kg?

## Homework Equations

Force Friction = μ*Force Normal
Δd= vt +0.5aΔt2

## The Attempt at a Solution

From what I know is that the force static friction is the total amount of force allowed without allowing it to slip.
Force Friction = μ*Force Normal
Force Friction = 0.673*(mass of top block*gravity)
Force Friction = 0.673*(2.54*9.8)
Force Friction = 16.75 N

Now F=ma
16.75/(mass of top+bottom)=a
16.75/4.44=a
3.77 m/s^2 = a

Now Δd= vt +0.5aΔt2
7.2= 0*t +0.5(3.77)Δt2
Solve for t...1.95 seconds...wrong...

What Am I doing wrong?

I believe all your formulas and calculations look correct but I would think about why it would be necessary to add both masses when looking for the acceleration. It is only the maximum acceleration of the top block that is needed.

Nbwx said:

## Homework Statement

The coefficient of static friction is 0.673 between the two blocks shown. The coefficient of kinetic friction between the lower block and the floor is 0.113. Force F causes both blocks to cross a distance of 7.20m, starting from rest. What is the least amount of time in which the motion can be completed without the top block sliding on the lower block, if the mass of the lower block is 1.90kg and the mass of the upper block is 2.54kg?

## Homework Equations

Force Friction = μ*Force Normal
Δd= vt +0.5aΔt2

## The Attempt at a Solution

From what I know is that the force static friction is the total amount of force allowed without allowing it to slip.
Force Friction = μ*Force Normal
Force Friction = 0.673*(mass of top block*gravity)
Force Friction = 0.673*(2.54*9.8)
Force Friction = 16.75 N

Now F=ma
16.75/(mass of top+bottom)=a
16.75/4.44=a
3.77 m/s^2 = a

Now Δd= vt +0.5aΔt2
7.2= 0*t +0.5(3.77)Δt2
Solve for t...1.95 seconds...wrong...

What Am I doing wrong?

Hi Nbwx, Welcome to Physics Forums.

Is the external force being applied to the top or bottom block (or is it your choice to choose)?

I believe the force is being applied to the top block.

Nbwx said:
I believe the force is being applied to the top block.

In that case the maximum horizontal force that can be transmitted to the bottom block via the top block is what? What force impedes the bottom block's motion? Can you draw a FBD for the bottom block including these forces?

## 1. What is friction?

Friction is a force that opposes the motion of an object when it comes into contact with another object or surface.

## 2. How does friction affect distance?

Friction can cause an object to slow down or stop, which can decrease the distance it travels. Additionally, friction can also cause an object to move in a different direction, thus changing the distance it travels.

## 3. What factors affect the amount of friction?

The amount of friction is affected by the type of surfaces that are in contact, the force pressing the surfaces together, and the roughness of the surfaces.

## 4. How does friction relate to time?

The amount of friction can affect the time it takes for an object to travel a certain distance. More friction can slow down an object, resulting in a longer time to reach the destination.

## 5. How can friction be reduced?

Friction can be reduced by using lubricants, such as oil or grease, between two surfaces. Additionally, making surfaces smoother or using materials with lower coefficients of friction can also decrease friction.

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