Two Resistances R1 = 3 Ω and R2 = 6 Ω are connected in series with an ideal battery supplying a voltage of ∆ = 9 Volts. Sketch t
his circuit diagram. Now, replace the two resistors with an equivalent resistance R connected to the same battery. Sketch this circuit. (a) What is current I in R? (b) What is the potential difference V across R? Using this information, answer the following questions about the original, two-resistor circuit. (c) What is the current I1 in R1? (d) What is the current I2 in R2? (e) What is the potential difference V1 across R1? (f) What is in the potential difference V2 across R2? (g) How are V1 and V2 related to the battery voltage? Comparing the two circuits: (h) How are I1 and I2 related to I? (i) How are V1 and V2 related to ∆?
Two Resistances R1 = 3 Ω and R2 = 6 Ω are connected in parallel with an ideal battery supplying a voltage of ∆ =
9 Volts. Now, replace the two resistors with an equivalent resistance R connected to the same battery. Sketch this circuit. (a) What is current I in R? (b) What is the potential difference V across R? Using this information, answer the following questions about the original, two-resistor circuit. (c) What is the current I1 in R1? (d) What is the current I2 in R2? (e) What is the potential difference V1 across R1? (f) What is in the potential difference V2 across R2? (g) How are V1 and V2 related to the battery voltage? Comparing the two circuits: (h) How are I1 and I2 related to I? (i) How are V1 and V2 related to ∆?
Two Resistances R1 = 3 Ω and R2 = 6 Ω are connected in parallel with an ideal battery supplying a voltage of ∆ =
9 Volts. Now, replace the two resistors with an equivalent resistance R connected to the same battery. Sketch this circuit. (a) What is current I in R? (b) What is the potential difference V across R? Using this information, answer the following questions about the original, two-resistor circuit. (c) What is the current I1 in R1? (d) What is the current I2 in R2? (e) What is the potential difference V1 across R1? (f) What is in the potential difference V2 across R2? (g) How are V1 and V2 related to the battery voltage? Comparing the two circuits: (h) How are I1 and I2 related to I? (i) How are V1 and V2 related to ∆?
1 answer:
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Explanation:
We assume that length of boat is L cm. And, we suppose to have a coordinate system relative to the bottom of the lake with:
Boat's position initially from x = 0 cm to x = L cm
Let person (S) is initially at x = L cm (right hand end of boat)
and, let boat's center of mass at x = C cm
Therefore, initially center of mass of overall (system's) is at where (taking moments about x = 0).
= 130C + 80L ........... (i)
After S walks left to the other end of the boat, the boat moves right 80 cm.
Hence,
Boat's position is now from x = 80 cm to x = (L+ 80) cm
S's position is x = 80 (left end of boat)
Boat's center of mass is at (C + 80).
Therefore, overall (system's) final center of mass is at where (taking moments about x = 0).
= ............. (ii)
As no external force is acted on the system, the system's center of mass has not moved, so .
This means the left hand sides of both equations (i) and (ii) are equal. So, we can equate the right hand sides giving: the equation as follows.
130C + 80L =
80L = 16800 cm
L = 210 cm
= 2.1 m
Length of boat = 2.1 m
When the person is walking from one end to the other as there was no external force then center of mass of the person-boat system did not move.