Answer:
E=252J
Explanation:
The total mechanical energy of an object or system is given by:
E mech=K+U
Where K is the kinetic energy of the object and U is the potential energy of the object. The carriage, sitting motionless at the top of the hill, has only potential energy in the form of gravitational potential energy.
Gravitational potential energy is given by:
Ug=mgh
Where m is the mass of the object, g is the gravitational acceleration constant, and h is the height of the object above some specific reference point, in this case the ground 21 m below.
The weight of a stationary object at the surface of the earth is equal to the force of gravity acting on the object.
W=→Fg=mg
We are given that the carriage weighs 12 N, therefore mg=12N.
Ug=12N⋅21m
⇒Ug=252Nm=252J
Hope it helped, God bless you!
Answer:

Explanation:
As we know that the magnetic field near the center of solenoid is given as

now we know that initially the length of the solenoid is L = 18 cm and N number of turns are wounded on it
So the magnetic field at the center of the solenoid is 2 mT
now we pulled the coils apart and the length of solenoid is increased as L = 21 cm
so we have

now plug in all values in it


The mass on the spring is 0.86 kg
Explanation:
The period of a mass-spring system is given by the equation

where
m is the mass
k is the spring constant
In this problem, we have:
k = 88.7 N/m is the spring constant
The system makes 15 oscillations in 9.24 s: therefore, the period of the system is

Now we can re-arrange the first equation to solve for the mass:

Learn more about period:
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