Answer:
a. 32.67 rad/s² b. 29.4 m/s²
Explanation:
a. The initial angular acceleration of the rod
Since torque τ = Iα = WL (since the weight of the rod W is the only force acting on the rod , so it gives it a torque, τ at distance L from the pivot )where I = rotational inertia of uniform rod about pivot = mL²/3 (moment of inertia about an axis through one end of the rod), α = initial angular acceleration, W = weight of rod = mg where m = mass of rod = 1.8 kg and g = acceleration due to gravity = 9.8 m/s² and L = length of rod = 90 cm = 0.9 m.
So, Iα = WL
mL²α/3 = mgL
dividing through by mL, we have
Lα/3 = g
multiplying both sides by 3, we have
Lα = 3g
dividing both sides by L, we have
α = 3g/L
Substituting the values of the variables, we have
α = 3g/L
= 3 × 9.8 m/s²/0.9 m
= 29.4/0.9 rad/s²
= 32.67 rad/s²
b. The initial linear acceleration of the right end of the rod?
The linear acceleration at the initial point is tangential, so a = Lα = 0.9 m × 32.67 rad/s² = 29.4 m/s²
Answer:
The electric current in the wire is 0.8 A
Explanation:
We solve this problem by applying the formula of the magnetic field generated at a distance by a long and straight conductor wire that carries electric current, as follows:
B= Magnetic field due to a straight and long wire that carries current
u= Free space permeability
I= Electrical current passing through the wire
a = Perpendicular distance from the wire to the point where the magnetic field is located
Magnetic Field Calculation
We cleared (I) of the formula (1):
Formula(2)
a =8cm=0.08m
We replace the known information in the formula (2)
I=0.8 A
Answer: The electric current in the wire is 0.8 A
Newton's law of conservation states that energy of an isolated system remains a constant. It can neither be created nor destroyed but can be transformed from one form to the other.
Implying the above law of conservation of energy in the case of pendulum we can conclude that at the bottom of the swing the entire potential energy gets converted to kinetic energy. Also the potential energy is zero at this point.
Mathematically also potential energy is represented as
Potential energy= mgh
Where m is the mass of the pendulum.
g is the acceleration due to gravity
h is the height from the bottom z the ground.
At the bottom of the swing,the height is zero, hence the potential energy is also zero.
The kinetic energy is represented mathematically as
Kinetic energy= 1/2 mv^2
Where m is the mass of the pendulum
v is the velocity of the pendulum
At the bottom the pendulum has the maximum velocity. Hence the kinetic energy is maximum at the bottom.
Energy can neither be created e destroyed. It can only be transferred from one form to another. Implying this law and the above explainations we conclude that at the bottom of the pendulum,the potential energy=0 and the kinetic energy=294J as the entire potential energy is converted to kinetic energy at the bottom.
Answer:
a =3.33 m/s²
Explanation:
given,
initial speed of Plane, u = 0 m/s
final speed of plane, v = 60 m/s
time of the acceleration, t = 18 s
average acceleration of the plane, a = ?
average acceleration is equal to change in velocity per unit time.
a =3.33 m/s²
Hence, average acceleration of the plane is equal to a =3.33 m/s²
The steps in order to calculate the mass of a given volume of water is to use density. <span>Density is a physical
property of a substance that represents the mass of that substance per unit
volume. It is a property that can be used to describe a substance. Density slightly varies with changes in temperature so that it is important to determine the temperature.</span>
