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In a cam-follower mechanism, the follower needs to rise through 20 mm during 60o of cam rotation, the first 30o with a constant acceleration and then with a deceleration of the same magnitude. The initial and final speeds of the follower are zero. The cam rotates at a uniform speed of 300 rpm. The maximum speed of the follower is
[GATE-2005]
- a)0.60m/s
- b)1.20m/s
- c)1.68m/s
- d)2.40m/s
Correct answer is option 'D'. Can you explain this answer?
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To find the maximum speed of the follower in a cam-follower mechanism, we need to consider the motion of the follower during the constant acceleration and deceleration phases.
Given:
- Rise of the follower = 20 mm
- Cam rotation during rise = 60 degrees
- Cam rotation speed = 300 rpm
- Initial and final speeds of the follower = 0
1. Calculate the time taken for the constant acceleration phase:
During the first 30 degrees of cam rotation, the follower rises through 20 mm. We can use the kinematic equation to find the time taken for this phase:
s = ut + (1/2)at^2
20 mm = 0 * t + (1/2) * a * (30/360)^2
20 mm = (1/2) * a * (1/12)^2
a = (20 mm * 12^2) / (2 * 1)
a = 1200 mm/s^2
2. Calculate the time taken for the deceleration phase:
During the next 30 degrees of cam rotation, the follower needs to come to rest. Since the deceleration is the same magnitude as the acceleration, the time taken will be the same as the constant acceleration phase.
3. Calculate the total time taken for the rise:
The total time taken for the rise can be calculated by adding the times taken for the constant acceleration and deceleration phases:
t_total = 2 * t_acceleration = 2 * (30/360) * 60 / (300/60)
t_total = 0.1 seconds
4. Calculate the maximum speed of the follower:
The maximum speed of the follower can be calculated using the equation of motion:
v = u + at
v = 0 + a * t_total
v = 1200 mm/s^2 * 0.1 s = 120 mm/s = 0.12 m/s
Therefore, the maximum speed of the follower is 0.12 m/s, which corresponds to option D.
Given:
- Rise of the follower = 20 mm
- Cam rotation during rise = 60 degrees
- Cam rotation speed = 300 rpm
- Initial and final speeds of the follower = 0
1. Calculate the time taken for the constant acceleration phase:
During the first 30 degrees of cam rotation, the follower rises through 20 mm. We can use the kinematic equation to find the time taken for this phase:
s = ut + (1/2)at^2
20 mm = 0 * t + (1/2) * a * (30/360)^2
20 mm = (1/2) * a * (1/12)^2
a = (20 mm * 12^2) / (2 * 1)
a = 1200 mm/s^2
2. Calculate the time taken for the deceleration phase:
During the next 30 degrees of cam rotation, the follower needs to come to rest. Since the deceleration is the same magnitude as the acceleration, the time taken will be the same as the constant acceleration phase.
3. Calculate the total time taken for the rise:
The total time taken for the rise can be calculated by adding the times taken for the constant acceleration and deceleration phases:
t_total = 2 * t_acceleration = 2 * (30/360) * 60 / (300/60)
t_total = 0.1 seconds
4. Calculate the maximum speed of the follower:
The maximum speed of the follower can be calculated using the equation of motion:
v = u + at
v = 0 + a * t_total
v = 1200 mm/s^2 * 0.1 s = 120 mm/s = 0.12 m/s
Therefore, the maximum speed of the follower is 0.12 m/s, which corresponds to option D.
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In a cam-follower mechanism, the follower needs to rise through 20 mm during 60o of cam rotation, the first 30o with a constant acceleration and then with a deceleration of the same magnitude. The initial and final speeds of the follower are zero. The cam rotates at a uniform speed of 300 rpm. The maximum speed of the follower is[GATE-2005]a)0.60m/sb)1.20m/sc)1.68m/sd)2.40m/sCorrect answer is option 'D'. Can you explain this answer?
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