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Answer:
The time constant is
Explanation:
From the question we are told that
The spring constant is 
The mass of the ball is 
The amplitude of the oscillation t the beginning is 
The amplitude after time t is 
The number of oscillation is 
Generally the time taken to attain the second amplitude is mathematically represented as
Here T is the period of oscillation

=> 
=> 
Generally the amplitude at time t is mathematically represented as

Here a is the damping constant so
at
, 
So

=> 
taking natural log of both sides
=>
=> 
Generally the time constant is mathematically represented as
=>
=>
Answer:
v=v0 - gt
Explanation:
The equation for velocity is
v=v0 - gt
where v0=14m/s, g=10m/s^2.
in 1 second:
v=14-10=4m/s
it is positive so direction is upwards
in 2 seconds:
v=14-20=-6m/s
it is negative so direction is downwards
The magnitude of work done by the gas is 279 J and the sign is negative so W = -279 J as work is done by the system.
<u>Explanation:</u>
According to first law of thermodynamics, the change in internal energy of the system is equal to the sum of the heat energy added or released from the system with the work done on or by the system. If the heat energy is added to the system to perform a certain work, then the heat energy is taken as positive, while it will be negative when the heat energy is released from the system.
Similarly, in this case, the heat energy of 597 J is added to the system. So the heat energy will be positive, while the gas expansion occurs means work is done by the system.
ΔU = Q+W
Since ΔU is the change in internal energy which is given as 318 J and the heat energy added to the system is Q = 597 J.
Then the work done by the gas = ΔU - Q = 318 J - 597 J = - 279 J.
As the work is done by the system, so it will be denoted in negative sign and the magnitude of work done by the gas is 279 J.
"An object weighs about two times as much on Jupiter as on Neptune." Hope this helps :)