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Answer:
θ = 19.66°
Explanation:
To determine the angle that the rope makes with the vertical for the two people, you first take into account the potential energy of the first person before he swings on the rope:
h: distance to the ground
g: gravitational acceleration = 9.8m/s^2
m: mass of the first person = 55 kg
In the image attache below you can notice that the height h is:
Then, the potential energy is:
When the first person picks up the second person (when the rope is exactly vertical), all the potential energy becomes kinetic energy. Next, when both people reaches the maximum height h' the energy must be equal to the initial potential energy of the first person:
From the previous equation you can get h':
Finally, you obtain the angle between the rope at the height h,' and the vertical, by calculating the following:
hence, the angle between the rope and the vertical, when the two people are in the rope is 19.66°
Answer:
16.1 m/s
Explanation:
We can solve the problem by using the law of conservation of energy.
At the beginning, the spring is compressed by x = 35 cm = 0.35 m, and it stores an elastic potential energy given by
where k = 316 N/m is the spring constant. Once the block is released, the spring returns to its natural length and all its elastic potential energy is converted into kinetic energy of the block (which starts moving). This kinetic energy is equal to
where m = 0.15 kg is the mass of the block and v is its speed.
Since the energy must be conserved, we can equate the initial elastic energy of the spring to the final kinetic energy of the block, and from the equation we obtain we can find the speed of the block: