A 0.180 kilogram cart traveling at 0.80 meter per second to the right collides with a 0.100 -kilogram cart initially at rest . T
1 answer:
The final velocity of the two carts is 0.51 m/s
Explanation:
We can solve the problem by using the law of conservation of momentum: in fact, the total momentum of the two carts must be conserved before and after the collision, in absence of external forces. Thus, we can write:
where:
is the mass of the first cart
is the initial velocity of the first cart
is the mass of the second cart
is the initial velocity of the second cart (at rest)
is the final combined velocity of the two carts
Re-arranging the equation and substituting the values, we find the final velocity of the two carts after the collision:
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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:
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Answer:
1.6 s
Explanation:
To find the time in which the potential difference of the inductor reaches 24V you use the following formula:
V_o: initial voltage = 60V
R: resistance = 24-Ω
L: inductance = 42H
V_L: final voltage = 24 V
You first use properties of the logarithms to get time t, next, replace the values of the parameter:
hence, after 1.6s the inductor will have a potential difference of 24V