7. A cube sits in the Cartesian coordinate system. Each side of the cubeis 2m. Electric charge is distributed in the cube with a
1 answer:
Answer:
Net charge inside the cube is 321.6 C
Explanation:
Given charge density function is ρ =
side of cube is 2m
According to the definition of volume charge density total charge is given by
q = total charge = where dv = dxdydz is the volume element
on substututing the respected values we get
q =
on solving the above integration we get
q = x
x
⇒ q = 321.6 C
Therefore net charge inside the cube is 321.6 C
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Answer:
A) 26.5 m/s
B) 33.0 m/s
Explanation:
A)
- Once the car leaves the cliff, as no other influence than gravity acts on it, and since it causes the car an acceleration in the vertical direction only, in the horizontal direction, it keeps moving at the same speed until it reaches to the other side.
- So, we can apply the definition of average velocity to find this speed as follows:
- We know the value of Δx, which is just the wide of the river (53.0m), but we need to find also the value of Δt.
- This time is given by the vertical movement, whic.h is independent from the horizontal one, because both movements are perpendicular each other.
- Since the only influence in the vertical direction is due to gravity, the car is accelerated by gravity, with constant acceleration downward equal to g = -9.8m/s² (taking the upward direction as positive).
- Since the acceleration is constant, we can use the following kinematic equation, as follows:
- if we take the river level as our x-axis, this means that yf = 1.3 m and
y₀ = 20.8 m.
- At the same time, due to in the vertical direction the car has no initial velocity, this means that v₀ = 0.
- Replacing by the values in (2) , and solving for t:
- If we choose t₀ =0 ⇒ Δt = t = 2 s
- Replacing Δx and Δt in (1):
B)
- When the car is just landing in the other side, the velocity of the car has two components, the horizontal one that we just found in A) and a vertical one.
- Due to the initial velocity in the vertical direction was just zero, we can find the final velocity just applying the definition of acceleration, with a =g, as follows:
- Since both components are perpendicular each other, we can find the magnitude of the velocity vector (the speed) using the Pythagorean Theorem, as follows: