a.) K 2=K 1 +GmM( r 21− r 11)=2.2×10 7J
b.) K 2 +GmM( r 11− r 21)=6.9×10 7 J
Applying Law of Energy conservation :
K 1+U 1
=K 2+U 2
⇒K 1− r 1GmM
=K 2− r 2 GmM
where M=5.0×10 23kg,r1
=> R=3.0×10 6m and m=10kg
(a) If K 1
=5.0×10 7J and r 2
=4.0×10 6 m, then the above equation leads to
K 2=K 1 +GmM (r 21− r 11)=2.2×10 7J
(b) In this case, we require K 2
=0 and r2
=8.0×10 6m, and solve for K 1:K 1
=K 2 +GmM (r 11− r 21)=6.9×10 7 J
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Answer:
P = 5880 J
Explanation:
Given that,
The mass of the block, m = 30 kg
The block is sitting at a height of 20 m.
The block will have gravitational potential energy. The formula for gravitational potential energy is given by :
So, the required potential energy is equal to 5880 J.
Answer:
Explanation:
Well you have the voltages right, and that is no trivial matter. Each one of the resistors in a parallel circuit sees the same input voltages (in this case 6).
Now I think it would be a good idea to fill in the the resistance column.
R1 = 3 ohms
R2 = 6 ohms
R3 = 2 ohms
The total resistance can be calculated in two ways. I'll get around to doing both of them but I'll do the conventional way first. One hint: the total resistance must be smaller than the smallest resistor. Read that sentence over a couple of times. What it means is that it must be less than 2 ohms in a parallel circuit.
1/r1 + 1/r2 + 1/r3 = 1/rt
1/3 + 1/6 + 1/2 = 1/rt
Change all the denominators to 6ths.
2/6 + 1/6 + 3/6 = 1/rt
(2 + 1 + 3)/6 = 6/6 = 1
rt = 1
====================
So the current I is V/R
V = 6
R = 1
Current = V/R = 6/1 = 6 amps.
====================
The current in each resistor is
I1 = V / R1
I1 = 6/3 = 2 amps
I2 = V/R2
I2 = 6/6 = 1 amp
I3 = 6/2 = 3 amps
The total is I1 + I2 + I3 = 2 + 1 + 3 = 6 amps.
======================
Remember I said there was 2 ways of figuring out the total resistance. I did one of them about. Here's the other.
R = V / It
R = 6 / 6
R = 1 ohm just what you got before.
====================
Power
P = V * I
P1 = 6 * 2 = 12 watts
P2 = 6*1 = 6 watts
P3 = 6*3 = 18 watts
Pt = 36 watts.
Pt can be done by using the voltage * the total current
Pt = 6 volts * 6 amps = 36 watts, just what you would expect.
Answer:
19.5 m/s
87.8 m
Explanation:
The acceleration of block one is:
∑F = ma
-m₁gμ = m₁a
a = -gμ
a = -(9.8 m/s²) (0.22)
a = -2.16 m/s²
The velocity of block one just before the collision is:
v² = v₀² + 2aΔx
v² = (8.25 m/s)² + 2 (-2.16 m/s²) (2.3 m)
v = 7.63 m/s
Momentum is conserved, so the velocity of block two just after the collision is:
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
m₁u₁ = m₂v₂
(18.5 kg) (7.63 m/s) = (7.25 kg) v
v = 19.5 m/s
The acceleration of block two is also -2.16 m/s², so the distance is:
v² = v₀² + 2aΔx
(0 m/s)² = (19.5 m/s)² + 2 (-2.16 m/s²) Δx
Δx = 87.8 m
Answer:
c. emission of electromagnetic radiation.
Explanation:
When an atom changes its state from an excited one to the ground state, it means that the atom is changing from a state with higher energy to a state of lower energy.
This can occur, for instance, in the presence of an electronic transition (an electron moving from a higher energy level to a lower energy state) or of a nuclear transition (the nucleus get de-excited). In both cases, since the total energy must be conserved, there must be energy released. This energy is released as a photon (electromagnetic radiation), whose energy is equal to the difference between the two energy levels involved in the transition.
