A vector starts at the point (0.0) and ends at (2,-7) what is the magnitude of the displacement
1 answer:
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Answer:
a. R1 = 0.162 Ω
b. R2 = 0.340 Ω
Explanation:
Since the resistors R1 and R2 are connected in series, the current flowing through them when the 9 V battery is applied is 9/R1 + R2.
When the current increases by 0.450 A wen only R1 is in the circuit, the current is
9/R1 + R2 + 0.450 A = 9/R1 (1)
When the current increases by 0.225 A when only R2 is in the circuit, the current is
9/R1 + R2 + 0.225 A = 9/R2 (2)
equation (1) - (2) equals
9(1/R1 - 1/R2) = 0.450 A - 0.225
9(1/R1 - 1/R2) = 0.125
(1/R1 - 1/R2) = 0.125 A/9 = 0.0138
1/R1 = 0.0138 + 1/R2
R1 = R2/(1 + 0.0138R2) (3)
From (1)
9/R1 - 9/R1 + R2 = 0.450 A
9R2/[R1(R1 + R2)] = 0.450 A
R2/[R1(R1 + R2)] = 0.450 A/9 = 0.5
R2/[R1(R1 + R2)] = 0.5 (4)
From (3) R2/R1 = (1 + 0.0138R2) and from (4) R2/R1 = 0.5(R1 + R2). So,
(1 + 0.0138R2) = 0.5(R1 + R2)
0.5R1 + 0.5R2 = 1 + 0.0138R2
0.5R1 = 1 + 0.0138R2 - 0.5R2
0.5R1 = 1 - 0.4862R2 (5)
Substituting (3) into (5) we have
0.5R2/(1 + 0.0138R2) = 1 - 0.4862R2
R2 = (1 + 0.0138R2)(1 - 0.4862R2)
R2 = 1 - 0.4724R2 - 0.0067R2²
Collecting like terms, we have
0.0067R2² + 0.4724R2 + R2 - 1 = 0
0.0067R2² + 1.4724R2 - 1 = 0
Using the quadratic formula,
We choose the positive answer.
So R2 = 0.340 Ω
From (5)
R1 = 0.5 - 0.9931R2
= 0.5 - 0.9931 × 0.340
= 0.5 - 0.338
= 0.162 Ω
a. R1 = 0.162 Ω
b. R2 = 0.340 Ω
Answer:
Explanation:
First of all, let's convert from nanometres to metres, keeping in mind that
So we have:
Now we can convert from metres to centimetres, keeping in mind that
So, we find:
The two ladybugs have same rotational (angular) speed
Explanation:
The rotational (angular) speed of an object in circular motion is defined as:
where
is the angular displacement
t is the time interval considered
Here we have two ladybugs, which are located at two different distances from the axis. In particular, ladybug 1 is halfway between ladybug 2 and the axis of rotation. However, since they rotate together with the disk, and the disk is a rigid body, every point of the disk cover the same angle in the same time
: this means that every point along the disk has the same angular speed, and therefore the two ladybugs also have the same angular speed.
On the other hand, the linear speed of the two ladybugs is different, because it follows the equation:
where r is the distance from the axis: and since the two ladybugs are located at different , they have different linear speed.
Learn more about circular motion:
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