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 angular velocity of the crank pin. We can use the formula:
Angular velocity (ω) = (Linear velocity) / (Radius)
The linear velocity is the speed of the locomotive, which is given as 100 km/h. We need to convert it to meters per second, so we divide by 3.6:
Linear velocity = 100 km/h ÷ 3.6 = 27.78 m/s
The radius is half the stroke of the piston. Given that the stroke is 600 mm, convert it to meters:
Radius = 600 mm ÷ 1000 = 0.6 m
Now we can calculate the angular velocity:
ω = 27.78 m/s ÷ 0.6 m = 46.3 rad/s
The centripetal acceleration (a) can be found using the equation:
Centripetal acceleration (a) = (Angular velocity)² × Radius
Plugging in the values:
a = (46.3 rad/s)² × 0.6 m
a = 2148.69 m²/s²
So, the centripetal acceleration of the crank pin relative to the engine frame is 2148.69 m²/s².