The mass of the roller coaster below is 80 kg. It starts from rest at a height of 30 m and reaches a speed of 20 m/s at point B. Assume no energy is lost due to dissipative forces such as friction. Also use g = 10 m/s2.
What is the total mechanical energy of the roller coaster cart at point A?
Energy is the same top and bottom, Ke at bottom, Pe at top
Pe = m g h = 80 * 10 * 30 Joules
the end.
To calculate the total mechanical energy of the roller coaster cart at point A, we need to consider the potential energy and the kinetic energy.
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.
To find the total mechanical energy of the roller coaster cart at point A, we need to consider the potential energy and the kinetic energy.
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.