Train Question: Max Acceleration 0.756m/s^2

[madahmad1]

1.A passenger train is traveling at 25m/s around a circular curve of 1000 m radius. if the maximum total acceleration is not to exceed g/10, determine the maximum rate at which the speed may be decreased. Take g = 9.81 m/s^2.

Answer is 0.756 m/s^2, but what steps do i take to find the answer?

 

[BishopUser]

centripetal acceleration equation and knowing how to add vectors is a good start

 

[Scrum]

Wow I actually got this one :)

You are given the velocity V of the Train (25m/s) and the radius R of the circle (1000m)
From this you can use the formula Radial Acceleration Arad = V^2 / R to get the Radial Acceleration (That is the acceleration toward the center of the circle to make the velocity change direction)

Plug those in and you will get Arad = .625

Now you know that you want the magnitude of total acceleration to be g/10 or .981, and you know one of the components of acceleration, Arad to be .625. Since you know both of these you can solve for the unknown component of acceleration which will be tangent to the circle

Sqrt( .625^2 + A^2 ) = .981

Do the algebra and you will get the answer to be .756 m/s^2
hopefully that makes sense.