Answer:
θ=5.65°
Explanation:
Given Data
Mass m=1.5 kg
Length L=0.80 m
First spring constant k₁=35 N/m
Second spring constant k₂=56 N/m
To find
Angle θ
Solution
As the both springs take half load so apply Hooks Law:
Force= Spring Constant ×Spring stretch
F=kx
x=F/k
as
θ=5.65°
17.
There are three different methods for charging objects:
- Friction: in friction, two objects are rubbed against each other. As a result, electrons can be passed from one object to the other, so one object will gain a net negative charge while the other object will gain a net positive charge due to the lack of electrons.
- Conduction: this occurs when two conductive objects are put in contact with each other, and charges (electrons, usually) are transferred from one object to the other one.
- Induction: this occurs when two objects are brought closer to each other, but not in contact. If one of the two objects has a net charge (different from zero) on its surface, then it will induce a movement of charges in the second object: in particular, in the second object, charges of the opposite polarity will be attracted towards the first object, while charges of same polarity will be repelled further away.
18.
Charged objects produce around themselves an electric field. The strenght of the electric field is given by (assuming the charged objects are spherical)
where k is the Coulomb's constant, q is the magnitude of the charge and r the distance from the centre of the charge. As we see, the strength of the field is inversely proportional to the square of the distance.
Also, the direction of the field is determined by the sign of the charge:
- if the charge is positive, the electric field points away from the charge (this means that other positive charges in the field will be repelled away)
- if the charge is negative, the electric field points towards the charge (this means that other positive charges in the field will be attracted towards it)
19.
Electrical force is given by:
where k is the Coulomb's constant, q1 and q2 are the two charges, and r their separation.
Gravitational force is given by:
where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r their separation.
Similarities between the two forces:
- Both are inversely proportional to the square of the distance between the two objects, r
- Both are non-contact forces (the two objects can experience the forces even if they are not in contact)
- Both forces have infinite range
Differencies between the two forces:
- The electric force can be either attractive or repulsive, while the gravitational force is attractive only
- The electric force is much stronger than the gravitational force, due to the much larger value of the Coulomb's constant k compared to the gravitational constant G
To solve this problem we will apply the concepts related to the electric field. This is defined as the product between the angular frequency, the number of turns of the body (solenoid in this case) the magnetic field and the sine of the angular frequency and time. Mathematically this can be described as
Here,
= Angular frequency
N = Number of turns
B = Magnetic field
The emf has its maximum value when
Thus the amplitude of the emf is
When number of turns of armature, area and applied magnetic field remains constant, induced emf is proportional to angular speed.
Further it can be written as follows,
Therefore the maximum amplitude of induced emf when armature rotates at 10.0rad/s is 18V