A locomotive is running at a constant speed of 100 km/ h. The diameter of driving wheels is 1.8 m. The

stroke of the piston of the steam engine cylinder of the locomotive is 600 mm. Find the centripetal
acceleration of the crank pin relative to the engine frame.

To find the centripetal acceleration of the crank pin relative to the engine frame, we need to first calculate the linear velocity of the crank pin.

The linear velocity of the crank pin can be determined using the formula:
Linear Velocity = Angular Velocity x Radius

The angular velocity can be calculated using the rotation speed of the locomotive's driving wheels. Since the locomotive is running at a constant speed, we can assume the rotation speed of the driving wheels is the same as the speed of the locomotive divided by the circumference of the driving wheels.

Angular Velocity = Speed of Locomotive ÷ Circumference of Driving Wheels

The circumference of the driving wheels can be calculated using the formula:
Circumference = π x Diameter of Driving Wheels

Now, we can calculate the linear velocity of the crank pin by substituting the values in the equation:
Linear Velocity = Angular Velocity x Radius

The radius of the crank pin can be calculated by considering the piston stroke. As the crank pin is connected to the piston, it moves in a circular arc that is directly proportional to the piston stroke. Thus, the radius of the crank pin is half of the piston stroke.

Now, by knowing the linear velocity, we can calculate the centripetal acceleration using the formula:
Centripetal Acceleration = (Linear Velocity^2) ÷ Radius

Substituting the known values, we can find the centripetal acceleration of the crank pin.