An automobile fuel tank is filled to the brim with 45 L of gasoline (12 gal) at 10°C. Immediately afterward, the vehicle is park
ed in the sunlight, where the temperature is 35°C. How much gasoline overflows from the tank as a result of the expansion? (Neglect the expansion of the tank.)
1 answer:
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Answer:
a) 4.2m/s
b) 5.0m/s
Explanation:
This problem is solved using the principle of conservation of linear momentum which states that in a closed system of colliding bodies, the sum of the total momenta before collision is equal to the sum of the total momenta after collision.
The problem is also an illustration of elastic collision where there is no loss in kinetic energy.
Equation (1) is a mathematical representation of the the principle of conservation of linear momentum for two colliding bodies of masses and
whose respective velocities before collision are
and
;
where and
are their respective velocities after collision.
Given;
Note that =0 because the second mass
was at rest before the collision.
Also, since the two masses are equal, we can say that so that equation (1) is reduced as follows;
m cancels out of both sides of equation (2), and we obtain the following;
a) When , we obtain the following by equation(3)
b) As stops moving
, therefore,
Answer:
ωf = 4.53 rad/s
Explanation:
By conservation of the angular momentum:
Ib*ωb = (Ib + Ic)*ωf
Where
Ib is the inertia of the ball
ωb is the initial angular velocity of the ball
Ic is the inertia of the catcher
ωf is the final angular velocity of the system
We need to calculate first Ib, Ic, ωb:
ωb = Vb / (L/2) = 16 / (1.2/2) = 26.67 m/s
Now, ωf will be: