Least amount of time for motion

In summary, the coefficient of static friction is 0.65 between two blocks and the coefficient of kinetic friction between the lower block and the floor is 0.20. A force applied to the top block causes both blocks to move a distance of 5.0 m, starting from rest. The least amount of time in which this motion can be completed without the top block sliding on the lower block is 1.657 seconds.
  • #1
aaphys
1
0

Homework Statement

: [/B]

The coefficient of static friction is 0.65 between two blocks. The coefficient of kinetic friction between the lower block and the floor is 0.20. Force
Fvec.gif
(a pull applied to the top block) causes both blocks to cross a distance of 5.0 m, starting from rest. What is the least amount of time in which this motion can be completed without the top block sliding on the lower block?

Let:
topBlock = m1
lowerBlock = m2

Given:
m1 = 4.0 kg
m2 = 3.0 kg
μs = 0.65
μk = 0.2
Δd = 5.0 m

Homework Equations

:[/B]
∑F = ma
Δd = (1/2)at^2

The Attempt at a Solution

:
[/B]
Starting with Δd = (0.5)at^2

a = [2Δd]/[t^2]

Now using ∑F = ma

ΣF = [m1+m2]*[a] = [m1+m2]*[2Δd]/[t^2]
ΣF = [2Δd*(m1+m2)]/t^2
t^2 = [2Δd*(m1+m2)]/[ΣF]

t^2 = [2*5*(4+3)]/[ΣF]
t^2 = [70]/[ΣF]

To find ΣF I said that the force applied must be one that is

m1gμs > F > (m1+m2)gμk → (4)*(9.8)*(0.65) > F > (4 + 3)*(9.8)*(0.2) → 25.48N > F > 13.72N

Then I use 25.48N and

t^2 = 70/25.48
t = √[70/25.48]
t= 1.657 s

And it's wrong :(
 
Physics news on Phys.org
  • #2
Your calculation looks correct to me. Maybe somebody else can spot a problem we missed, or maybe the answer in the book is wrong.
 
  • Like
Likes aaphys
  • #3
andrewkirk said:
Your calculation looks correct to me. Maybe somebody else can spot a problem we missed, or maybe the answer in the book is wrong.
I also got the same answer.
 
  • Like
Likes aaphys

FAQ: Least amount of time for motion

1. What is the definition of "least amount of time for motion"?

The least amount of time for motion refers to the minimum amount of time that is required for an object to move from one position to another. It is also known as the minimum time of travel or the shortest time of motion.

2. How is the least amount of time for motion calculated?

The least amount of time for motion is calculated by dividing the distance traveled by the speed of the object. This formula is represented as t = d/s, where t is the time, d is the distance, and s is the speed.

3. Can the least amount of time for motion be negative?

No, the least amount of time for motion cannot be negative. Time is always a positive quantity, and the concept of negative time does not exist in physics.

4. What factors affect the least amount of time for motion?

The least amount of time for motion is affected by the speed of the object, the distance it needs to travel, and any external forces acting on the object such as friction or air resistance. The faster the object moves and the shorter the distance it needs to travel, the shorter the time of motion will be.

5. Is the least amount of time for motion constant?

No, the least amount of time for motion is not constant. It can vary depending on the factors mentioned above. For example, if the speed or distance changes, the least amount of time for motion will also change. It is only constant if all the factors remain the same.

Similar threads

Back
Top