Answer:
R = 9.85 ohm , r = 0.85 ohm
Explanation:
Let the two resistances by r and R.
when they are connected in series:
V = 12 V
i = 1.12 A
The equivalent resistance when they are connected in series is
Rs = r + R
So, By using Ohm's law
V = i Rs
Rs = V / i = 12 / 1.12 = 10.7 ohm
R + r = 10.7 ohm .... (1)
When they are connected in parallel:
V = 12 V
i = 9.39 A
The equivalent resistance when they are connected in parallel
So, By using Ohm's law
V = i Rp
Rp = V / i = 12 / 9.39 = 1.28 ohm
.... (2)
by substituting the value of R + r from equation (1) in equation (2), we get
r R = 8.36 ..... (3)
..... (4)
By solvng equation (1) and (4), we get
R = 9.85 ohm , r = 0.85 ohm
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Answer:
Power_input = 85.71 [W]
Explanation:
To be able to solve this problem we must first find the work done. Work is defined as the product of force by distance.
where:
W = work [J] (units of Joules)
F = force [N] (units of Newton)
d = distance [m]
We need to bear in mind that the force can be calculated by multiplying the mass by the gravity acceleration.
Now replacing:
![W = (80*10)*3\\W = 2400 [J]](https://tex.z-dn.net/?f=W%20%3D%20%2880%2A10%29%2A3%5C%5CW%20%3D%202400%20%5BJ%5D)
Power is defined as the work done over a certain time. In this way by means of the following formula, we can calculate the required power.
where:
P = power [W] (units of watts)
W = work [J]
t = time = 40 [s]
![P = 2400/40\\P = 60 [W]](https://tex.z-dn.net/?f=P%20%3D%202400%2F40%5C%5CP%20%3D%2060%20%5BW%5D)
The calculated power is the required power. Now as we have the efficiency of the machine, we can calculate the power that is introduced, to be able to do that work.
![Effic=0.7\\Effic=P_{required}/P_{introduced}\\P_{introduced}=60/0.7\\P_{introduced}=85.71[W]](https://tex.z-dn.net/?f=Effic%3D0.7%5C%5CEffic%3DP_%7Brequired%7D%2FP_%7Bintroduced%7D%5C%5CP_%7Bintroduced%7D%3D60%2F0.7%5C%5CP_%7Bintroduced%7D%3D85.71%5BW%5D)
The addition of vectors involve both magnitude and direction. In this case, we make use of a triangle to visualize the problem. The length of two sides were given while the measure of the angle between the two sides can be derived. We then assign variables for each of the given quantities.
Let:
b = length of one side = 8 m
c = length of one side = 6 m
A = angle between b and c = 90°-25° = 75°
We then use the cosine law to find the length of the unknown side. The cosine law results to the formula: a^2 = b^2 + c^2 -2*b*c*cos(A). Substituting the values, we then have: a = sqrt[(8)^2 + (6)^2 -2(8)(6)cos(75°)]. Finally, we have a = 8.6691 m.
Next, we make use of the sine law to get the angle, B, which is opposite to the side B. The sine law results to the formula: sin(A)/a = sin(B)/b and consequently, sin(75)/8.6691 = sin(B)/8. We then get B = 63.0464°. However, the direction of the resultant vector is given by the angle Θ which is Θ = 90° - 63.0464° = 26.9536°.
In summary, the resultant vector has a magnitude of 8.6691 m and it makes an angle equal to 26.9536° with the x-axis.
