Tarzan (75 kg) swings from 4 metres high on a vine down to ground level and catches Jane (50 kg). How fast are they moving after
1 answer:
Try this solution (if it is possible, check it in other sources):
1. for m_Tarzan=75kg., initial_height=4m., end_height=0 m. and g=10 N/kg. Energy is:
2. The same value of Energy is applied for m_Tarzan+Jane=75+50=125 kg.:
3. According to the formula of the Speed:
Speed=sqrt(6000/125)=sqrt(48)=4sqrt(3)≈4*1.71=6.84 (m/s)
Answer: 6.84 (m. per sec.)
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Answer:
The maximum acceleration of the system is 359.970 centimeters per square second.
Explanation:
The motion of the mass-spring system is represented by the following formula:
Where:
- Position of the mass with respect to the equilibrium position, measured in centimeters.
- Amplitude of the mass-spring system, measured in centimeters.
- Angular frequency, measured in radians per second.
- Time, measured in seconds.
- Phase, measured in radians.
The acceleration experimented by the mass is obtained by deriving the position equation twice:
Where the maximum acceleration of the system is represented by .
The natural frequency of the mass-spring system is:
Where:
- Spring constant, measured in newtons per meter.
- Mass, measured in kilograms.
If and
, the natural frequency is:
Lastly, the maximum acceleration of the system is:
The maximum acceleration of the system is 359.970 centimeters per square second.