Answer : Maximum height of the pendulum is 0.43 m
Explanation :
Given that,
Mass of the pendulum, m = 2 kg
Speed of the pendulum, v = 2.9 m/s
When it reaches the lowest point on its path, the potential energy at the highest point is equal to the kinetic energy at the lowest point.
i.e.
h is the height of the pendulum.
Hence, this is the required solution.
The average current density in the wire is given by:
where I is the current intensity and A is the cross-sectional area of the wire.
The cross-sectional area of the wire is given by:
where r is the radius of the wire. In this problem, , so the cross-sectional area is
and the average current density is
A lady bug moves 10 cm forward and 5 cm backwards
so total distance moved by lady bug = 10 + 5 = 15 cm
total time taken by the lady bug
t = 20 s
so the average speed is given as
so its average speed is 0.75 cm/s
Electric charge on the plastic cube:
Explanation:
The electric potential around a charged sphere (such as the Van der Graaf) generator is given by
where
k is the Coulomb's constant
Q is the charge on the sphere
r is the distance from the centre of the sphere
Here we have:
V = 200,000 V on the surface of the sphere, so at r = 12.0 cm
We need to find the voltage V' at 2.0 cm from the edge of the sphere, so at
r' = 12.0 + 2.0 = 14.0 cm
Since the voltage is inversely proportional to r, we can use:
This is the potential at the location of the plastic cube.
Now we can use the law of conservation of energy, which states that the initial electric potential energy of the cube is totally converted into kinetic energy when the plastic cube is at infinite distance from the generator. So we can write:
where:
q is the charge on the plastic cube
V' is the potential at the location of the cube
m = 5.0 g = 0.005 kg is the mass of the cube
v = 3.0 m/s is the final speed of the cube
Solving for q, we find the charge on the cube:
Learn more about electric fields:
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