In a roller coaster ride cars and passengers slide down an incline of 36 degrees to horizontal if the friction is negligible find magnitude of acceleration
To find the magnitude of acceleration, we will use the basic principles of physics related to inclined planes. The acceleration of the roller coaster can be determined using the following equation:
acceleration = g * sin(theta)
Where:
- acceleration is the magnitude of acceleration
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- theta is the angle of the incline (36 degrees in this case)
Now, let's substitute the values into the equation:
acceleration = 9.8 m/s^2 * sin(36 degrees)
To find the sine of 36 degrees, you can use a scientific calculator or the trigonometric function on your calculator. The sine of 36 degrees is approximately 0.588.
acceleration = 9.8 m/s^2 * 0.588 ≈ 5.748 m/s^2
So, the magnitude of the acceleration is approximately 5.748 m/s^2.