A parallel-plate capacitor with capacitance C 0 stores charge of magnitude Q 0 on plates of area A 0 separated by distance d 0 . The potential difference across the plates is Δ V 0 . If the capacitor is attached to a battery and the charge is doubled to 2 Q 0 , what are the ratios (a) C new / C 0 and (b) ΔV new /Δ V 0 ? A second capacitor is identical to the first capacitor except the plate area is doubled to 2 A 0 . If given a charge of Q 0 , what are the ratios (c) C new / C 0 and (d) Δ V new /Δ V 0 ? A third capacitor is identical to the first capacitor, except the distance between the plates is doubled to 2 d 0 . If the third capacitor is then given a charge of Q 0 , what are the ratios (e) C new / C 0 and (f) Δ V new /Δ V 0 ?
A parallel-plate capacitor with capacitance C 0 stores charge of magnitude Q 0 on plates of area A 0 separated by distance d 0 . The potential difference across the plates is Δ V 0 . If the capacitor is attached to a battery and the charge is doubled to 2 Q 0 , what are the ratios (a) C new / C 0 and (b) ΔV new /Δ V 0 ? A second capacitor is identical to the first capacitor except the plate area is doubled to 2 A 0 . If given a charge of Q 0 , what are the ratios (c) C new / C 0 and (d) Δ V new /Δ V 0 ? A third capacitor is identical to the first capacitor, except the distance between the plates is doubled to 2 d 0 . If the third capacitor is then given a charge of Q 0 , what are the ratios (e) C new / C 0 and (f) Δ V new /Δ V 0 ?
Solution Summary: The author explains that the capacitance depends on the area and the distance of separation of the plates.
A parallel-plate capacitor with capacitance C0 stores charge of magnitude Q0 on plates of area A0 separated by distance d0. The potential difference across the plates is ΔV0. If the capacitor is attached to a battery and the charge is doubled to 2Q0, what are the ratios (a) Cnew/C0 and (b) ΔVnew/ΔV0? A second capacitor is identical to the first capacitor except the plate area is doubled to 2A0. If given a charge of Q0, what are the ratios (c) Cnew/C0 and (d) ΔVnew/ΔV0? A third capacitor is identical to the first capacitor, except the distance between the plates is doubled to 2d0. If the third capacitor is then given a charge of Q0, what are the ratios (e) Cnew/C0 and (f) ΔVnew/ΔV0?
Part C
Find the height yi
from which the rock was launched.
Express your answer in meters to three significant figures.
Learning Goal:
To practice Problem-Solving Strategy 4.1 for projectile motion problems.
A rock thrown with speed 12.0 m/s and launch angle 30.0 ∘ (above the horizontal) travels a horizontal distance of d = 19.0 m before hitting the ground. From what height was the rock thrown? Use the value g = 9.800 m/s2 for the free-fall acceleration.
PROBLEM-SOLVING STRATEGY 4.1 Projectile motion problems
MODEL: Is it reasonable to ignore air resistance? If so, use the projectile motion model.
VISUALIZE: Establish a coordinate system with the x-axis horizontal and the y-axis vertical. Define symbols and identify what the problem is trying to find. For a launch at angle θ, the initial velocity components are vix=v0cosθ and viy=v0sinθ.
SOLVE: The acceleration is known: ax=0 and ay=−g. Thus, the problem becomes one of…
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