To solve this problem, apply the concepts related to Hooke's law. From there we will find the spring constant. Subsequently, applying Energy balance, which includes gravitational potential energy, elastic potential energy and kinetic energy, we will bury the system's energy. Finally, using the displacement expression for the simple harmonic movement, we will find the expression that describes the system.
PART A) The expression for the spring force is

Here,
k = Spring constant
x = Displacement
Rearranging to find the spring constant we have that



PART B ) The gravitational potential energy acts on the spring holds the cart is zero. Since cart is placed in the equilibrium position. The kinetic energy of the cart is zero. Therefore the expression for the total energy is,




PART C) The expression for the angular frequency is



The equation for the motion of the cart is

Replacing,

Answer:
Approximately 6.8 x 10⁻¹⁵
Explanation:
To be able to get this fraction, there are some things we need to know.
1. The radius of nucleus = 1.0 x 10⁻¹³ cm
2. The radius of hydrogen atom = 52.9 pm
3. Volume of sphere = V1/V2 = (R1/R2)^3
4. 1 picometer (pm) = 10^-10 cm
CHECK ATTACHMENT FOR Step by step solution to the answer
Kinetic energy: the energy of motion
Work: the change in kinetic energy
Power: the rate of work done
Explanation:
The kinetic energy of an object is the energy possessed by the object due to its motion. Mathematically, it is given by:

where
m is the mass of the object
v is its speed
The work done an object is the amount of energy transferred; according to the energy-work theorem, it is equal to the change in kinetic energy of an object:

where
is the final kinetic energy
is the initial kinetic energy
Finally, the power is the rate of work done per unit time. Mathematically, ti can be expressed as

where
W is the work done
t is the time elapsed
Learn more about kinetic energy, work and power:
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Acceleration =
(change of speed) / (time for the change).
Change of speed = (speed at the end) - (speed at the beginning)
= ( zero ) - (40 m/s)
= -40 m/s .
Acceleration = (-40 m/s) / (5 seconds)
= -8 m/s² .
Answer: y will change the slowest but still with a zero (0) value.
Explanation: at y = 3: the height y will change the slowest when the coffee level is at the top of the cone.