Question

The roller coaster car reaches point A of the loop with speed of 20 m/s, which is increasing at the rate of 5 m/s2. Determine the magnitude of the acceleration at A if pA

Answer 1

Answer and Explanation:

Data provided as per the question is as follows

Speed at point A = 20 m/s

Acceleration at point C =
`5 m/s^2`

`r_A = 25 m`

The calculation of the magnitude of the acceleration at A is shown below:-

Centripetal acceleration is

`a_c = (v^2)/(r)`

now we will put the values into the above formula

=
`(20^2)/(25)`

After solving the above equation we will get

`= 16 m/s^2`

Tangential acceleration is

`= √(ac^2 + at^2) \\\\ = √(16^2 + 5^2)\\\\ = 16.703 m/s^2`