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,
Assuming the woman starts at rest, she descends the slide with acceleration <em>a</em> such that
(20.3 m/s)² = 2 <em>a</em> (42.6 m) → <em>a</em> ≈ 4.84 m/s²
which points parallel to the slide.
The only forces acting on her, parallel to the slide, are
• the parallel component of her weight, <em>w</em> (//)
• friction, <em>f</em>, opposing her descent and pointing up the slide
Take the downward sliding direction to be positive. By Newton's second law, the net force in the parallel direction acting on the woman is
∑ <em>F</em> (//) = <em>w </em>(//) - <em>f</em> = <em>ma</em>
where <em>m</em> = 77.0 kg is the woman's mass.
Solve for <em>f</em> :
<em>mg</em> sin(42.3°) - <em>f</em> = <em>ma</em>
<em>f</em> = <em>m</em> (<em>g</em> sin(42.3°) - <em>a</em>)
<em>f</em> = (77.0 kg) ((9.80 m/s²) sin(42.3°) - 4.84 m/s²) ≈ 135 N
Compute the work <em>W</em> done by friction: multiply the magnitude of the friction by the length of the slide.
<em>W</em> = (135 N) (42.6 m) ≈ 5770 N•m = 5770 J
It intimidates other spider because it makes them look bigger than they really are.
Answer: Temperature inversion
Explanation: Temperature inversion is a reverse of the normal temperature flow or distribution of the air,it usually causes temperature to rise as altitude increase towards the troposphere instead of reduction of temperature.
Temperature inversion is caused when warm,dense air flow above cold,less dense air. Temperature inversion is hazardous to man as it traps pollutants close to the Earth surface,this condition limits vertical circulation.
The kinetic energy is transferred to thermal energy through friction
