A magician pulls a tablecloth out from under some dishes. How far do the dishes move during the 0.25 it takes to pull out the tablecloth? The coefficient of kinetic friction between the cloth and the dishes is = 0.14.
KE= W(fr),
KE = m•v²/2,
W(fr) =
m•v²/2 = k•m•g•s .
v = a•t =k•g•t,
mv²/2 =m•( k•g•t)/2.
s = m•v²/2• k•m•g =
=m•( k•g•t)/2• k•m•g =
= g•t²•k/2 =
=9.8•(0.25)² •0.14/2 = 0.043 m/s.
To find out how far the dishes move during the 0.25 seconds it takes to pull out the tablecloth, we can use the following formula:
Distance = Velocity × Time
In this case, the velocity is the initial speed of the dishes due to the magician pulling the tablecloth.
To calculate the initial speed, we need to consider the forces acting on the dishes. When the tablecloth is pulled, there are two forces in play: the applied force pulling the tablecloth and the force of friction between the cloth and the dishes.
The applied force is responsible for the acceleration of the dishes, while the force of friction slows them down.
To find the applied force, we can use Newton's second law of motion:
Force = Mass × Acceleration
In this case, the mass we need to consider is the mass of the dishes.
Now, let's calculate the applied force:
Force = Mass × Acceleration
Acceleration is the change in velocity over time. Since the dishes start from rest (zero initial velocity), the final velocity will also be zero. Therefore, the change in velocity is:
Change in Velocity = Final Velocity - Initial Velocity
= 0 - 0 = 0
Since the change in velocity is zero, the acceleration is zero as well.
Force = Mass × 0
= 0
The applied force required to pull the tablecloth is zero since there is no acceleration.
Now, let's calculate the force of friction:
Force of Friction = Coefficient of Friction × Normal Force
The normal force is the force exerted by any object resting on a surface. In this case, it is the weight of the dishes acting vertically downward.
Now, let's calculate the force of friction:
Force of Friction = Coefficient of Friction × Normal Force
Before we can find the normal force, we need to know the mass of the dishes and the acceleration due to gravity.
Now, let's calculate the normal force:
Normal Force = Mass × Acceleration due to Gravity
Now, let's plug in the values:
Normal Force = Mass × 9.8 m/s²
Finally, we can calculate the force of friction:
Force of Friction = Coefficient of Friction × Normal Force
Now that we have the force of friction, we can calculate the distance the dishes move using the following formula:
Distance = (Initial Velocity × Time) + (0.5 × Acceleration × Time²)
Since the dishes start from rest (initial velocity is zero), the equation simplifies to:
Distance = 0.5 × Acceleration × Time²
Now, let's plug in the values and calculate the distance the dishes move:
Distance = 0.5 × Acceleration × Time²
Keep in mind that the acceleration is determined by the force of friction, which is calculated earlier.
By following this step-by-step process, you should be able to find the distance the dishes move during the 0.25 seconds it takes to pull out the tablecloth.