Answer:
a) see attached, a = g sin θ
b)
c) v = √(2gL (1-cos θ))
Explanation:
In the attached we can see the forces on the sphere, which are the attention of the bar that is perpendicular to the movement and the weight of the sphere that is vertical at all times. To solve this problem, a reference system is created with one axis parallel to the bar and the other perpendicular to the rod, the weight of decomposing in this reference system and the linear acceleration is given by
Wₓ = m a
W sin θ = m a
a = g sin θ
b) The diagram is the same, the only thing that changes is the angle that is less
θ' = 9/2 θ
c) At this point the weight and the force of the bar are in the same line of action, so that at linear acceleration it is zero, even when the pendulum has velocity v, so it follows its path.
The easiest way to find linear speed is to use conservation of energy
Highest point
Em₀ = mg h = mg L (1-cos tea)
Lowest point
Emf = K = ½ m v²
Em₀ = Emf
g L (1-cos θ) = v² / 2
v = √(2gL (1-cos θ))
Answer:
The magnitude of the voltage is
and the direction of the current is clockwise.
Explanation:
Given that,
Number of turns = 9
Magnetic field = 0.5 T
Diameter = 3 cm
Time t = 0.14 s
We need to calculate the flux
Using formula of flux

Put the value into the formula


We need to calculate the emf
Using formula of emf




Negative sign shows the direction of current.
Hence, The magnitude of the voltage is
and the direction of the current is clockwise.
Answer:
Pressure of the gas = 12669 (Pa) and height of the oil is 1,24 meters
Explanation:
First, we can use the following sketch for an easy understanding, in the attached image we can see the two pressure gauges the one with mercury to the right and the other one with oil to left. We have all the information needed in the mercury pressure gauge, so we can determine the pressure inside the vessel because the fluid is a gas it will have the same pressure distributed inside the vessel (P1).
Since P1 = Pgas, we can use the same formula, but this time we need to determine the height of the column of oil in the pressure gauge.
The result is that the height of the oil column is higher than the height of the one that uses mercury, this is due to the higher density of mercury compared to oil.
Note: the information given in the units of the fluids is not correct because the density is always expressed in units of (mass /volume)
Full outer shell of electrons, they are colorless and odorless ,their melting and boiling points are close together which gives them very narrow liquid range
Explanation:
Let us assume that the mass of a pitched ball is 0.145 kg.
Initial velocity of the pitched ball, u = 47.5 m/s
Final speed of the ball, v = -51.5 m/s (in opposite direction)
We need to find the magnitude of the change in momentum of the ball and the impulse applied to it by the bat. The change in momentum of the ball is given by :

So, the magnitude of the change in momentum of the ball is 14.355 kg-m/s.
Let the the ball remains in contact with the bat for 2.00 ms. The impulse is given by :

Hence, this is the required solution.