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 determine the linear speed of the crank pin and the radius of its circular path.
First, let's find the linear speed of the crankpin:
- The speed of the locomotive is given as 100 km/h.
- Convert this to meters per second: 100 km/h * (1000 m/1 km) * (1 h / 3600 s) = 27.78 m/s.
Next, let's calculate the radius of the circular path:
- The stroke of the piston of the steam engine cylinder is given as 600 mm.
- Convert this to meters: 600 mm * (1 m/1000 mm) = 0.6 m.
- The radius of the crank pin's circular path is half the stroke of the piston: 0.6 m / 2 = 0.3 m.
Now, we can find the centripetal acceleration using the formula:
Centripetal acceleration = (linear speed)^2 / radius
Plugging in the values:
Centripetal acceleration = (27.78 m/s)^2 / 0.3 m
Centripetal acceleration = 769.29 m^2/s^2 / 0.3 m
Centripetal acceleration = 2564.3 m/s^2
Therefore, the centripetal acceleration of the crank pin relative to the engine frame is approximately 2564.3 m/s^2.