Answer:
The maximum possible speed of the truck at the foot of the mountain at 550 m above sea level is 135.91 [tex]\frac{m}{s}[/tex]
Explanation:
Mechanical energy is the ability of a body to generate motion and perform mechanical work.
In other words, mechanical energy is that related to both the position and the movement of bodies.
Mechanical energy is calculated by:
Em = Ep + Ec
where Em is the mechanical energy (J), Ep the potential energy (J) and Ec the kinetic energy (J).
The mechanical energy of a body remains constant when all the forces acting on it are conservative.
Potential energy refers to the position of a mass in space and is calculated by:
Ep = m • g • h
where m is the mass (kg), g the gravity of the Earth (9.81 [tex]\frac{m}{s^{2} }[/tex]) and h is the height (m)
Kinetic energy is the energy that an object has due to its movement and its expression for the calculation is:
Ec = ½ m • v²
Where m is the mass (Kg) and v the speed (m/s).
The truck would have the maximum possible speed if friction were ignored. Then:
So the forces are conservative and the mechanical energy is constant. So:
Em initial= Em final
So:
Ep initial + Ec initial= Ep final + Ec final
m • g • h initial + ½ m • (v initial)² = m • g • h final + ½ m • (v final)² [mass and gravity remain constant]
As the mass m is found in all terms, they can be simplified and it is obtained:
g • h initial + ½ • (v initial)² = g • h final + ½ • (v final)²
Taking as a reference the zero of the potential energy at sea level and isolating the value of vf, you obtain the expression:
[tex]vfinal=\sqrt{(v initial)^{2} +2*g*(h initial - h final)}[/tex]
Being:
and replacing:
[tex]vfinal=\sqrt{(15 \frac{m}{s} )^{2} +2*9.81 \frac{m}{s^{2} } *(1480 m - 550 m)}[/tex]
you get:
v final= 135.91 [tex]\frac{m}{s}[/tex]
The maximum possible speed of the truck at the foot of the mountain at 550 m above sea level is 135.91 [tex]\frac{m}{s}[/tex]
