An amusement park ride spins you around in a circle of radius 2.5 m with a speed of 8.5 m/s. If your mass is 75 kg, what is the
2 answers:
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Answer:
1. False 2) greater than. 3) less than 4) less than
Explanation:
1)
- As the collision is perfectly elastic, kinetic energy must be conserved.
- The expression for the final velocity of the mass m₁, for a perfectly elastic collision, is as follows:
- As it can be seen, as m₁ ≠ m₂, v₁f ≠ 0.
2)
- As total momentum must be conserved, we can see that as m₂ > m₁, from the equation above the final momentum of m₁ has an opposite sign to the initial one, so the momentum of m₂ must be greater than the initial momentum of m₁, to keep both sides of the equation balanced.
3)
- The maximum energy stored in the in the spring is given by the following expression:
- where A = maximum compression of the spring.
- This energy is always the sum of the elastic potential energy and the kinetic energy of the mass (in absence of friction).
- When the spring is in a relaxed state, the speed of the mass is maximum, so, its kinetic energy is maximum too.
- Just prior to compress the spring, this kinetic energy is the kinetic energy of m₂, immediately after the collision.
- As total kinetic energy must be conserved, the following condition must be met:
- So, it is clear that KE₂f < KE₁₀
- Therefore, the maximum energy stored in the spring is less than the initial energy in m₁.
4)
- As explained above, if total kinetic energy must be conserved:
- So as kinetic energy is always positive, KEf₂ < KE₁₀.
Answer:
2.45 m
Explanation:
First of all, we have to calculate the time of flight of the book, by using the equation for the vertical motion:
where
h = 1.19 m is the vertical distance covered by the book
g = 9.8 m/s^2 is the acceleration of gravity
t is the time of flight
Solving for t,
Now we can find the horizontal distance covered by the book, which is given by
where
is the horizontal velocity
t = 0.49 s is the time of flight
Substituting,
So the book lands 2.45 m away.
Hello!
A stretched spring has 5184 J of elastic potential energy and a spring constant of 16,200 N/m. What is the displacement of the spring?
0.57 m
0.64 m
0.80 m
1.25 m
Data:
For a spring (or an elastic), the elastic potential energy is calculated by the following expression:
Where k represents the elastic constant of the spring (or elastic) and x the deformation or displacement suffered by the spring.
Solving:
Answer:
The displacement of the spring = 0.8 m (or 0.80 m)
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