Energy is the same top and bottom, Ke at bottom, Pe at top
Pe = m g h = 80 * 10 * 30 Joules
the end.
What is the total mechanical energy of the roller coaster cart at point A?
Pe = m g h = 80 * 10 * 30 Joules
the end.
1. Potential Energy (PE):
The potential energy at point A is given by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
Given that the mass of the roller coaster cart is 80 kg, the acceleration due to gravity is 10 m/s^2, and the height is 30 m, we can calculate the potential energy:
PE = 80 kg * 10 m/s^2 * 30 m = 24,000 J.
2. Kinetic Energy (KE):
The roller coaster starts from rest at point A, so its initial kinetic energy is zero.
Total Mechanical Energy (TME):
The total mechanical energy is the sum of the potential energy and the kinetic energy, which can be calculated as:
TME = PE + KE.
Since the initial kinetic energy is zero, we can simplify the equation to:
TME = PE = 24,000 J.
Therefore, the total mechanical energy of the roller coaster cart at point A is 24,000 J.
The potential energy (PE) of an object is given by the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above a reference point. In this case, the reference point is taken as the ground, so h = 30 m.
So, the potential energy at point A is given by PE = (80 kg)(10 m/s^2)(30 m) = 24000 J.
The kinetic energy (KE) of an object is given by the formula KE = 1/2 mv^2, where m is the mass of the object and v is its velocity.
Since the roller coaster starts from rest, its initial velocity at point A is 0 m/s. Therefore, the kinetic energy at point A is KE = 1/2 (80 kg)(0 m/s)^2 = 0 J.
Since no energy is lost due to dissipative forces such as friction, the total mechanical energy at point A is equal to the sum of the potential energy and the kinetic energy, which is 24000 J + 0 J = 24000 J.
Therefore, the total mechanical energy of the roller coaster cart at point A is 24000 Joules.