To find the centripetal acceleration of the crank pin relative to the engine frame, we need to first calculate the angular velocity of the driving wheels.
The circumference of the driving wheel can be calculated using the formula:
C = πd
Where C is the circumference and d is the diameter of the driving wheel.
Given that the diameter of the driving wheel is 1.8 m, we can calculate the circumference as follows:
C = π * 1.8 = 5.6549 m
Now, let's find the distance covered by the locomotive in one revolution of the driving wheel. Since the circumference of the wheel is equal to the distance traveled in one revolution, the distance traveled in one revolution is also equal to 5.6549 m.
Next, we need to find the time taken for one revolution. We know that the locomotive is running at a constant speed of 100 km/h, which means it covers 100 km in one hour. Since distance = speed * time, we can solve for time:
100 km = (100 km/h) * t
t = 1 hour
However, we need the time taken for one revolution, so we need to convert the time from hours to seconds:
1 hour = 60 minutes * 60 seconds = 3600 seconds
Now, we can calculate the angular velocity (ω) of the driving wheel using the formula:
ω = (2π) / T
Where ω is the angular velocity and T is the time taken for one revolution.
Plugging in the values, we get:
ω = (2π) / 3600 = 0.001745 rad/s
To find the centripetal acceleration of the crank pin (ac), we need to know the distance of the crank pin from the center of rotation. In this case, the stroke of the piston (600 mm) gives us this distance.
The centripetal acceleration can be calculated using the formula:
ac = r * ω^2
Where ac is the centripetal acceleration, r is the distance of the crank pin from the center of rotation, and ω is the angular velocity.
Converting the stroke of the piston from millimeters to meters, we get:
r = 600 mm = 0.6 m
Plugging in the values, we can calculate the centripetal acceleration:
ac = (0.6 m) * (0.001745 rad/s)^2 = 0.001447 m/s^2
Therefore, the centripetal acceleration of the crank pin relative to the engine frame is approximately 0.001447 m/s^2.