The concept required to perform this exercise is given by the coulomb law.
The force expressed according to this law is given by
Where,
q = charges of the objects
r= distance/radius
Our values are previously given, so
Replacing,
The force acting on the block are given by,
Therefore the box is accelerated upward.
Complete Question
For each of the following scenarios, describe the force providing the centripetal force for the motion:
a. a car making a turn
b. a child swinging around a pole
c. a person sitting on a bench facing the center of a carousel
d. a rock swinging on a string
e. the Earth orbiting the Sun.
Answer:
Considering a
The force providing the centripetal force is the frictional force on the tires \
i.e
where is the coefficient of static friction
Considering b
The force providing the centripetal force is the force experienced by the boys hand on the pole
Considering c
The force providing the centripetal force is the normal from the bench due to the boys weight
Considering d
The force providing the centripetal force is the tension on the string
Considering e
The force providing the centripetal force is the force of gravity between the earth and the sun
Explanation:
Explanation:
A) To prove the motion of the center of mass of the cylinders is simple harmonic:
System diagram for given situation is shown in attached Fig. 1
We can prove the motion of the center of mass of the cylinders is simple harmonic if
where aₓ is acceleration when attached cylinders move in horizontal direction:
<h3>PROOF:</h3>rotational inertia for cylinders is given as:
-----(1)
Newton's second law for angular motion is:
∑τ = Iα ------(2)
For linear motion in horizontal direction it is:
∑Fₓ = Maₓ ------ (3)
By definition of torque:
τ = RF --------(4)
Put (4) and (1) in (2)
from Fig 3 it can be seen that fs is force by which the cylinders roll without slipping as they oscillate
So above equation becomes
------ (5)
As angular acceleration is related to linear by:
Eq (5) becomes
---- (6)
aₓ shows displacement in horizontal direction
From (3)
∑Fₓ = Maₓ
Fₓ is sum of fs and restoring force that spring exerts:
----(7)
Put (7) in (3)
[/tex] -----(8)
Using (6) in (8)
--- (9)
For spring mass system
----- (10)
Equating (9) and (10)
then (9) becomes
(The minus sign says that x and aₓ have opposite directions as shown in fig 3)
This proves that the motion of the center of mass of the cylinders is simple harmonic.
<h3 /><h3>B) Time Period</h3>Time period is related to angular frequency as:
Answer:
See the explanation below
Explanation:
To better understand this problem, a cylinder sketch is attached before and after the cut, we see that after the cut, the shape of this resembles that of a right triangle.
We can find, the centroid in the xy plane, knowing that the centroid for a triangle is located a third of its base.
In the z axis there is no displacement of the centroid.
