A bus travels from El Paso, Texas, to Chihuahua, Mexico, in 5.2 h with an average velocity of 73 km/h to the south. What is the
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Answer:
The spring constant is 4159.02 N/m.
Explanation:
Given:
Mass of the ball (m) = 79.5 g = 0.0795 kg [1 g = 0.001 kg]
Height of the ball above spring (h) = 51.3 cm = 0.513 m [1 cm = 0.01 m]
Compression in the spring (x) = 4.57537 cm = 0.0457537 m
Total vertical displacement of the ball is equal to the sum of height above spring and compression of the spring. So,
Total vertical height (h+x) = 51.3 cm + 4.57537 cm = 55.87537 cm = 0.5587537 m
Now, as per energy conservation, the total energy of the ball at any position is always a constant.
So, energy possessed by the ball the highest point is equal to the energy possessed by the ball at the lowest point.
Energy at the highest point is due to gravitational potential energy only and energy at the lowest point is due to elastic potential energy only.
So, GPE = EPE
Here 'k' is the spring constant.
Now, plug in all the values and solve for 'k'. This gives,
Therefore, the spring constant is 4159.02 N/m.
Answer:
We first to know that if the wheel rotates from rest means that at t=0 the velocity and the angle rotated is 0.
Then, we know:
Integrating 2 times, we have:
For the first 27.9 s, we have:
w = 37.107 rad/s
angle = 517.6426 rad
For the next seconds, according to the text, the angular velocity is constant so
w = 37.107 rad/s and hence, integrating:
Then, the time remaining is:
53.5 - 27.9 = 25.6
So for the next 25.6 seconds we have:
Finally, we add the 2 angles and we have as a result: