As an ice skater begins a spin, his angular speed is 3.14 rad/s. After pulling in his arms, his angular speed increases to 5.94
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
Hello!
A 10-kg cart moving at 5 m/s collides with a 5-kg cart at rest and causes it to move 10 m/s. Which principle explains the result? A) law of differential mass B) law of conservation of momentum C) law of unequal forces D) law of accelerated collision
We have the following data¹:
ΔP (momentum before impact) = ?
mA (mass) = 10 kg
vA (velocity) = 5 m/s
mB (mass) = 5 kg
vB (velocity) = 0 m/s
Solving:
ΔP = mA*vA + mB*vB
ΔP = 10 kg*5 m/s + 5 kg*0 m/s
ΔP = 50 kg*m/s + 0 kg*m/s
Δp = 50 kg*m/s ← (momentum before impact)
We have the following data²:
ΔP (momentum after impact) = ?
mA (mass) = 10 kg
vA (velocity) = 0 m/s
mB (mass) = 5 kg
vB (velocity) = 10 m/s
Solving:
Δp = mA*vA + mB*vB
Δp = 10 kg*0 m/s + 5 kg*10 m/s
Δp = 0 kg*m/s + 50 kg*m/s
Δp = 50 kg*m/s ← (momentum after impact)
*** Then, which principle explains the result ?
Law of conservation of momentum, <u>since the total momentum of body A and B before impact is equal to the total momentum of body A and B after impact.</u>
Note: Bodies of different masses and velocities may have the same kinetic energy, if proportionality between the units is maintained it can occur that they have the same kinetic energy.
Answer:
B) law of conservation of momentum
_______________________
Answer:162.516 gm
Explanation:
Given
Quartz contains 46.7 % silicon by mass
i.e.Silicon is 46.7 % by mass
Total mass of Quartz m=348 gm
46.7% of 348 gm