Answer:
The expected dynamic error is 0.019
The phase shift is -23.10°C
Explanation:
The explanation is shown on the first uploaded image
The deceleration experienced by the gymnast is the 9 times of the acceleration due to gravity.
Now from Newton`s first law, the net force on gymnast,

Here, W is the weight of the gymnast and a is the acceleration experienced by the gymnast (
acceleration due to gravity)
Therefore,
OR 
Given
and
Substituting these values in above formula and calculate the force exerted by the gymnast,


Answer: a) vcar= 7 m/s ; b) a train= 0.65 m/s^2
Explanation: By using the kinematic equation for the car and the train we can determine the above values of the car velocity and the acceletarion of the train, respectively.
We have for the car
distance = v car* t, considering the length of train (81.1 m) travel by the car during the first 11.6 s
the v car = distance/time= 81.1 m/11.6s= 7 m/s
In order to calculate the acceleration we have to use the kinematic equation for the train from the rest
distance train = (a* t^2)/2
distance train : distance travel by the car at constant speed
so distance train= (vcar*36.35)m=421 m
the a traiin= (2* 421 m)/(36s)^2=0.65 m/s^2
The original kinetic energy will be 0 J and the final kinetic energy will be 7500 J and the amount of work utilized will be similar to the final kinetic energy i.e., 7500 J.
<u>Explanation:</u>
As it is known that the kinetic energy is defined as the energy exhibited by the moving objects. So the kinetic energy is equal to the product of mass and square of the velocity attained by the car. Thus,

So the initial kinetic energy will be the energy exerted by the car at the initial state when the initial velocity is zero. Thus the initial kinetic energy will be zero.
The final kinetic energy is
= 7500 J
As the work done is the energy required to start the car from zero velocity to 5 m/s velocity.
Work done = Final Kinetic energy - Initial Kinetic energy
Thus the work utilized for moving the car is
Work done = 7500 J - 0 J = 7500 J
Thus, the initial kinetic energy of the car is zero, the final kinetic energy is 7500 J and the work utilized by the car is also 7500 J.
Explanation:
In first case, the forces on LHS and on RHS is the same i.e. 3 N. The force acting on the car is balanced force. As a result, the car will not move at all.
In second case,
Force on RHS = 2000 N
Force on LHS = -6000 N
Net force acting on it is given by :
F = 2000+(-6000)
= -4000 N
Hence, this is the required solution.