Explanation:
The total distance travelled by an object divided by total time taken is called the speed of an object. Its formula is given by :
Speed is a scalar quantity. It has only magnitude but no direction.
The total displacement of the particle divided by total time taken is called the velocity of that object. It is given by :
D is the displacement or shortest path covered
Velocity is a vector quantity. It have both magnitude and direction.
Both speed and velocity of an object are same. The only difference is that the speed is a scalar quantity while the velocity is a vector.
The statement that best explains the difference between velocity and speed is (A) i.e. "Velocity is speed with a direction".
The two different isotopes have weights :
w1 = 78.918 amu
w2 = 80.916 amu
average weight w3 = 79.903 amu
The mixing of two components can be modeled as
let the fraction of w1 be 'x'
hence
now this is a linear equation in 'x'. Substituting the values we get
x = 0.507
hence the percentage of Br79 = 50.7% and the percentage of BR81 = 49.3%
(a) -0.211 m
At the beginning the mass is displaced such that the length of the pendulum is L = 36.1 cm and the angle with the vertical is
The projection of the length of the pendulum along the vertical direction is
the full length of the pendulum when the mass is at the lowest position is
L = 36.1 cm
So the y-displacement of the mass is
(b) 0.347 J
The work done by gravity is equal to the decrease in gravitational potential energy of the mass, which is equal to
where we have
m = 168 g = 0.168 kg is the mass of the pendulum
g = 9.8 m/s^2 is the acceleration due to gravity
is the vertical displacement of the pendulum
So, the work done by gravity is
And the sign is positive, since the force of gravity (downward) is in the same direction as the vertical displacement of the mass.
(c) Zero
The work done by a force is:
where
F is the magnitude of the force
d is the displacement
is the angle between the direction of the force and the displacement
In this situation, the tension in the string always points in a radial direction (towards the pivot of the pendulum), while the displacement of the mass is tangential (it follows a circular trajectory): this means that the tension and the displacement are always perpendicular to each other, so in the formula
and so the work done is zero.
Answer: 1010.92 m/s
Explanation:
According to Newton's law of universal gravitation:
(1)
Where:
is the gravitational force between Earth and Moon
is the Gravitational Constant
is the mass of the Earth
is the mass of the Moon
is the distance between the Earth and Moon
Asuming the orbit of the Moon around the Earth is a circular orbit, the Earth exerts a centripetal force on the moon, which is equal to :
(2)
Where is the centripetal acceleration given by:
(3)
Being the orbital velocity of the moon
Making (1)=(2):
(4)
Simplifying:
(5)
Making (5)=(3):
(6)
Finding :
(7)
(8)
Finally: