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Leviafan [203]
3 years ago
9

A wire is used as a heating element that has a resistance that is fairly independent of its temperature within its operating ran

ge. When a current I flows through the wire, the energy delivered by the heater each minute is E. For what amount of current will the energy delivered by the heater each minute be 4E?
Physics
1 answer:
dedylja [7]3 years ago
3 0

Answer:

Double the current

Explanation:

The energy delivered by the heater is related to the current by the following relation:

E= I^{2}R t

let R * t = k ( ∴ R and t both are constant)

so E= k I^{2}

Now let:

E2= k I₂^2

E2= 4E

⇒ k I₂^2= 4* k I^{2}

Cancel same terms on both sides.

I₂^2= 4* I^{2}

taking square-root on both sides.

√I₂^2 = √4* I^2

⇒I₂= 2I

If we double the current the energy delivered each minute be 4E.

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Since F₁ = 5.2 N and acts at 53.7° below the negative axis in the third quadrant, its x-component is -F₂cos53.7° and its y- component is -F₂sin53.7°

Part A

What is the x component Fx of the resultant force?

The x component of the resultant force Fx = -F₁cos57° + -F₂cos53.7° = -9.2cos57° + (-5.2cos53.7°) = (-5.011 - 3.078) N = -8.089 N

Part B

What is the y component Fy of the resultant force?

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Part C  

What is the magnitude F of the resultant force?

The magnitude F of the resultant force = √(Fx² + Fy²)

F = √(-8.089² N + 3.525² N) = √65.432 + 12.426 = √77.858 = 8.824 N

Part D

What is the angle ? that the resultant force forms with the negative x axis?

The angle the resultant force makes with the negative x axis is given by

θ = tan⁻¹(Fy/Fx) = tan⁻¹(3.525/-8.089) = tan⁻¹-0.4358 = -23.55°.

To measure it from the negative x axis, we add 360. So, our angle = 360 -23.55 = 336.45°

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