The car shown in the figure has a mass of 395 kg when it passes through point A with a speed of 17.7 m/s, being the height of A 7.2 m above the ground (y = 0). In the instant that passes through C its speed is diminished to 7.6 m/s. Assuming that the path has no friction
(a) What is the height of point C?
(b) What is the mechanical energy at point B relative to the ground?
I already solved a part which gave me 20.24m
I need help with part b, thanks in advance!
at start
E = (1/2) m v^2 + m g h
E = (1/2)(395)(17.7)^2 + 395*9.81*7.2
= 61875 + 27900 = 89775 Joules
at C
89775 = (1/2)395(7.6)^2+395*9.81*h
h = [ 89775 - 11408] / (3875)
h = 20.22
so agree but part b is trivial:
89775 is the total mechanical energy forever and ever by the way if there is not friction
Yes, I forgot about the concept of conservation. Thank you!
But, but, conservation is in your title !!!!
To calculate the mechanical energy at point B relative to the ground, we need to consider the concept of mechanical energy.
Mechanical energy consists of two components: kinetic energy (KE) and gravitational potential energy (PE).
(a) To determine the height of point C, we will use the principle of conservation of mechanical energy. According to this principle, the total mechanical energy remains constant as long as no external forces, like friction, are acting on the car.
At point A, the total mechanical energy (E₁) is given by the sum of kinetic energy and gravitational potential energy:
E₁ = KE + PE = 1/2 * m * v₁² + m * g * h₁
where m is the mass of the car, v₁ is the velocity at point A, g is the acceleration due to gravity, and h₁ is the height at point A.
At point C, the total mechanical energy (E₂) is given by:
E₂ = KE + PE = 1/2 * m * v₂² + m * g * h₂
where v₂ is the velocity at point C, and h₂ is the height at point C (which we need to find).
Since no external forces are acting on the car, the mechanical energy at point A (E₁) is equal to the mechanical energy at point C (E₂):
E₁ = E₂
1/2 * m * v₁² + m * g * h₁ = 1/2 * m * v₂² + m * g * h₂
Substituting the given values:
1/2 * 395 kg * (17.7 m/s)² + 395 kg * 9.8 m/s² * 7.2 m = 1/2 * 395 kg * (7.6 m/s)² + 395 kg * 9.8 m/s² * h₂
Solving for h₂ will give us the height of point C.
(b) Now, let's calculate the mechanical energy at point B relative to the ground (E_B).
Again, using the principle of conservation of mechanical energy, the mechanical energy at point B (E_B) is equal to the mechanical energy at point A (E₁):
E_B = E₁
Since we already calculated the mechanical energy at point A (E₁), we can substitute its value to find E_B.
Therefore, the mechanical energy at point B relative to the ground is given by:
E_B = E₁ = 1/2 * m * v₁² + m * g * h₁
Substituting the known values will give us the answer to part (b).