Question

Q4

A railway truck is to round a curve on a level track, The radius of the curve is 120m, and the
track width is 1.8m. If the centre of gravity of then truck is 1.75m above the rails,
what is the maximum speed at which the truck can travel on the bend without overturning?

Answer 1

The maximum speed at which the truck can travel on the bend without overturning is approximately 37.4 m/s.

Explanation:

To determine the maximum speed at which the truck can travel on the bend without overturning, we need to consider the centripetal force acting on the truck and compare it to the gravitational force.

Given:

Radius of the curve (r): 120 m

Track width (d): 1.8 m

Height of the center of gravity above the rails (h): 1.75 m

First, let's calculate the maximum lateral acceleration the truck can withstand without tipping over. This can be determined by finding the difference in gravitational force acting on the truck and the centrifugal force acting outward.

Gravitational force (Fg):

The gravitational force acting on the truck is given by the equation Fg = m * g, where m is the mass of the truck and g is the acceleration due to gravity (approximately 9.8 m/s²).

Centripetal force (Fc):

The centripetal force acting on the truck is given by the equation Fc = m * a, where m is the mass of the truck and a is the acceleration towards the center of the curve.

Centrifugal force (Fcf):

The centrifugal force acting outward is given by the equation Fcf = m * ω² * r, where m is the mass of the truck, ω is the angular velocity, and r is the radius of the curve.

For the truck to remain stable, the maximum lateral acceleration (a) should not exceed the gravitational acceleration (g). So, we can equate the centripetal force to the gravitational force:

m * a = m * g

Next, we'll calculate the angular velocity (ω) using the relationship between linear velocity (v) and angular velocity:

v = ω * r

Now, let's solve for the maximum velocity (v) at which the truck can travel on the bend without overturning:

Centripetal force (Fc):

m * a = m * g

a = g

Centrifugal force (Fcf):

Fcf = m * ω² * r

Since a = g and v = ω * r, we can substitute these values into the equation for the centrifugal force:

m * g = m * v² / r

Simplifying the equation:

g = v² / r

Rearranging the equation to solve for the maximum velocity (v):

v² = g * r

v = √(g * r)

Now, let's substitute the given values:

g ≈ 9.8 m/s²

r = 120 m

v = √(9.8 * 120)

v ≈ 37.4 m/s

Therefore, the maximum speed at which the truck can travel on the bend without overturning is approximately 37.4 m/s.