Question

A 50 kg roller coaster car is launched, from ground level, at 20 m/s. How fast will it be moving when it reaches the top of a loop, which is 12 m above the ground?

Answer 1

The speed of the roller coaster at the top of the loop is approximately 8.66 m/s.

Step-by-step explanation:

To find the speed of the roller coaster when it reaches the top of the loop, we can use the concept of conservation of mechanical energy. At the top of the loop, the roller coaster has gravitational potential energy and kinetic energy. The gravitational potential energy is given by mgh, where m is the mass (50 kg), g is the acceleration due to gravity (9.8 m/s²), and h is the height (12 m above the ground). The kinetic energy is given by (1/2)mv², where m is the mass and v is the velocity.

Since mechanical energy is conserved, we can equate the initial and final energies:

mgh + (1/2)mv₀² = (1/2)mv²

Plugging in the values, we have:

(50 kg)(9.8 m/s²)(12 m) + (1/2)(50 kg)(20 m/s)² = (1/2)(50 kg)v²

Solving for v, we find that the speed of the roller coaster at the top of the loop is approximately 8.66 m/s.