Answer:
1. 12 V
2a. R₁ = 4 Ω
2b. V₁ = 4 V
3a. A = 1.5 A
3b. R₂ = 4 Ω
4. Diagram is not complete
Explanation:
1. Determination of V
Current (I) = 2 A
Resistor (R) = 6 Ω
Voltage (V) =?
V = IR
V = 2 × 6
V = 12 V
2. We'll begin by calculating the equivalent resistance. This can be obtained as follow:
Voltage (V) = 12 V
Current (I) = 1 A
Equivalent resistance (R) =?
V = IR
12 = 1 × R
R = 12 Ω
a. Determination of R₁
Equivalent resistance (R) = 12 Ω
Resistor 2 (R₂) = 8 Ω
Resistor 1 (R₁) =?
R = R₁ + R₂ (series arrangement)
12 = R₁ + 8
Collect like terms
12 – 8 =
4 = R₁
R₁ = 4 Ω
b. Determination of V₁
Current (I) = 1 A
Resistor 1 (R₁) = 4 Ω
Voltage 1 (V₁) =?
V₁ = IR₁
V₁ = 1 × 4
V₁ = 4 V
3a. Determination of the current.
Since the connections are in series arrangement, the same current will flow through each resistor. Thus, the ammeter reading can be obtained as follow:
Resistor 1 (R₁) = 4 Ω
Voltage 1 (V₁) = 6 V
Current (I) =?
V₁ = IR₁
6 = 4 × I
Divide both side by 4
I = 6 / 4
I = 1.5 A
Thus, the ammeter (A) reading is 1.5 A
b. Determination of R₂
We'll begin by calculating the voltage cross R₂. This can be obtained as follow:
Total voltage (V) = 12 V
Voltage 1 (V₁) = 6 V
Voltage 2 (V₂) =?
V = V₁ + V₂ (series arrangement)
12 = 6 + V₂
Collect like terms
12 – 6 = V₂
6 = V₂
V₂ = 6 V
Finally, we shall determine R₂. This can be obtained as follow:
Voltage 2 (V₂) = 6 V
Current (I) = 1.5 A
Resistor 2 (R₂) =?
V₂ = IR₂
6 = 1.5 × R₂
Divide both side by 1.5
R₂ = 6 / 1.5
R₂ = 4 Ω
4. The diagram is not complete
Answer:
A) 1.4167 × 10^(-11) F
B) r_a = 0.031 m
C) E = 3.181 × 10⁴ N/C
Explanation:
We are given;
Charge;Q = 3.40 nC = 3.4 × 10^(-9) C
Potential difference;V = 240 V
Inner radius of outer sphere;r_b = 4.1 cm = 0.041 m
A) The formula for capacitance is given by;
C = Q/V
C = (3.4 × 10^(-9))/240
C = 1.4167 × 10^(-11) F
B) To find the radius of the inner sphere,we will make use of the formula for capacitance of spherical coordinates.
C = (4πε_o)/(1/r_a - 1/r_b)
Rearranging, we have;
(1/r_a - 1/r_b) = (4πε_o)/C
ε_o is a constant with a value of 8.85 × 10^(−12) C²/N.m
Plugging in the relevant values, we have;
(1/r_a - 1/0.041) = (4π × 8.85 × 10^(−12) )/(1.4167 × 10^(-11))
(1/r_a) - 24.3902 = 7.8501
1/r_a = 7.8501 + 24.3902
1/r_a = 32.2403
r_a = 1/32.2403
r_a = 0.031 m
C) Formula for Electric field just outside the surface of the inner sphere is given by;
E = kQ/r_a²
Where k is a constant value of 8.99 × 10^(9) Nm²/C²
Thus;
E = (8.99 × 10^(9) × 3.4 × 10^(-9))/0.031²
E = 3.181 × 10⁴ N/C
Jupiter ............................................
Answer:
A) v₁ = 10.1 m/s t₁= 4.0 s
B) x₂= 17.2 m
C) v₂=7.1 m/s
D) x₂=7.5 m
Explanation:
A)
- Assuming no friction, total mechanical energy must keep constant, so the following is always true:
- Choosing the ground level as our zero reference level, Uf =0.
- Since the child starts from rest, K₀ = 0.
- From (1), ΔU becomes:
- In the same way, ΔK becomes:
- Replacing (2) and (3) in (1), and simplifying, we get:
- In order to find v₁, we need first to find h, the height of the slide.
- From the definition of sine of an angle, taking the slide as a right triangle, we can find the height h, knowing the distance that the child slides down the slope, x₁, as follows:
Replacing (5) in (4) and solving for v₁, we get:
- As this speed is achieved when all the energy is kinetic, i.e. at the bottom of the first slide, this is the answer we were looking for.
- Now, in order to finish A) we need to find the time that the child used to reach to that point, since she started to slide at the its top.
- We can do this in more than one way, but a very simple one is using kinematic equations.
- If we assume that the acceleration is constant (which is true due the child is only accelerated by gravity), we can use the following equation:
- Since v₀ = 0 (the child starts from rest) we can solve for a:
- Since v₀ = 0, applying the definition of acceleration, if we choose t₀=0, we can find t as follows:
B)
- Since we know the initial speed for this part, the acceleration, and the time, we can use the kinematic equation for displacement, as follows:
- Replacing the values of v₁ = 10.1 m/s, t₂= 2.0s and a₂=-1.5m/s2 in (10):
C)
- From (6) and (8), applying the definition for acceleration, we can find the speed of the child whem she started up the second slope, as follows:
D)
- Assuming no friction, all the kinetic energy when she started to go up the second slope, becomes gravitational potential energy when she reaches to the maximum height (her speed becomes zero at that point), so we can write the following equation:
- Replacing from (12) in (13), we can solve for h₂:
- Since we know that the slide makes an angle of 20º with the horizontal, we can find the distance traveled up the slope applying the definition of sine of an angle, as follows:
Answer:
the correct affirmation is the 3
Explanation:
Let's analyze the problem with Newton's second law before looking at the claims.
X axis parallel to the plane, positive down
F -fr + Wₓ = ma
Y Axis perpendicular to the plane
N -Wy = 0
With trigonometry
Wₓ = W sin θ
Wy = w cos θ
Let's multiply by the displacement along the plane, to relate to the work, which has as expression W = F d
F d -fr d + Wx d = ma d
Push W₁ = Fd
frictional force W₂ = -fr d
gravity W₃ = Wx d
W₁ + W₃ -W₂ = m a d
Analysis affirmations:
R1) false. The work of gravity is the subtraction
R2) false. Each force contributes according to its magnitude
R3) true. In the equation we see that, if the acceleration is zero, W2 = W1 + W3
R4) False. It equals the difference
the correct affirmation is the 3
