the tension ratio between the tight and slack side is 4,2:1. the force in the slack side of the belt is 500N. the diameter of the driving pulley is 350mm. the rotational frequency of the driving pulley is 550r/min
To calculate the tension in the tight side of the belt, we'll use the tension ratio and the force in the slack side.
Given:
Tension ratio between tight and slack side = 4.2:1
Force in slack side = 500N
Step 1: Calculate tension in the slack side of the belt
The tension in the slack side is given as 500N.
Tension in slack side = 500N
Step 2: Calculate tension in the tight side of the belt
Using the tension ratio, we can calculate the tension in the tight side.
Tension ratio = Tension in tight side / Tension in slack side
Tension in tight side = Tension ratio * Tension in slack side
= (4.2/1) * 500N
= 2100N
Tension in tight side = 2100N
Step 3: Calculate linear velocity of the belt
To calculate the linear velocity of the belt, we need to find the circumference of the driving pulley.
Circumference of the driving pulley = 2π * radius of the driving pulley
Given: Diameter of the driving pulley = 350mm
Radius of the driving pulley = Diameter / 2 = 350mm / 2 = 175mm = 0.175m
Circumference of the driving pulley = 2π * 0.175m = 1.1m (approx.)
Step 4: Calculate the distance traveled by the belt in one minute
The distance traveled by the belt in one minute is equal to the linear velocity of the belt multiplied by the rotational frequency of the driving pulley.
Distance traveled in one minute = Linear velocity * rotational frequency
Given: Rotational frequency of the driving pulley = 550r/min
Distance traveled in one minute = 1.1m * 550/min = 605m (approx.)
So, the distance traveled by the belt in one minute is approximately 605 meters.
To find the force on the tight side of the belt, we need to use the tension ratio between the tight and slack side, and the force on the slack side.
The tension ratio is given as 4.2:1. This means that for every unit of force on the slack side, there are 4.2 units of force on the tight side.
Given that the force on the slack side is 500N, we can calculate the force on the tight side:
Force on the tight side = Tension ratio * Force on the slack side
= 4.2 * 500N
= 2100N
The force on the tight side of the belt is 2100N.
Now, let's calculate the linear velocity of the driving pulley using the rotational frequency and the diameter of the pulley.
The rotational frequency is given as 550 revolutions per minute (r/min). To convert this to radians per second, we need to multiply by 2π/60.
Rotational frequency in radians per second = (550 r/min) * (2π/60)
= 57.78 radians/second
Next, we need to find the circumference of the driving pulley. The circumference is given by:
Circumference = π * diameter
= π * 350mm
= 1100 mm
The linear velocity of the driving pulley is given by:
Linear velocity = Rotational frequency * Circumference
= (57.78 radians/second) * (1100 mm)
= 63558 mm/s
Therefore, the linear velocity of the driving pulley is 63558 mm/s.