Draw a block and tackle system of pulleys with a velocity ratio of 5.A block and tackle with a velocity ratio of 5 is used to raise a mass of 25kg through a vertical distanceof 40cm at a steady rate. If the efforts is equal to 60N, determine
a)d distance moved by the effort
b)the work done by the effort in lifting the load
c)the loss in energy involved in lifting the load.
velocity ratio of 5 implies a distance ratio of 5
5 * 0.40 m = 2 m
work done by arms = 60*2 = 120 Joules
work done by lift on mass = 25*9.81*0.20
= 49.05 Joules
loss in energy = 120 - 49 = 71 Joules
how do you get Your question b answer
It has been so helpful to me.
To draw a block and tackle system of pulleys with a velocity ratio of 5, you would first start with the suspended mass, which in this case is 25kg. Next, you would connect this mass to the fixed object or ceiling using a rope or cable. Within the system, there will be multiple pulleys used to create the mechanical advantage.
The block and tackle system consists of two types of pulleys: the fixed pulley and the movable pulleys. The fixed pulley is attached to the fixed object or ceiling, and it does not move. The movable pulley, on the other hand, moves with the load as it is being lifted.
To achieve the velocity ratio of 5, you can use a combination of fixed and movable pulleys. One common configuration is to have one fixed pulley attached to the ceiling, and two movable pulleys attached to the load. The rope or cable would pass around the fixed pulley, then go down to the first movable pulley, back up to the fixed pulley, down to the second movable pulley, and finally back up to the person pulling on the rope.
Now, let's solve the given problem step by step:
a) To determine the distance moved by the effort, we need to calculate the mechanical advantage of the block and tackle system. The mechanical advantage can be calculated using the formula:
Mechanical Advantage = (Number of supporting ropes) * (Number of movable pulleys)
From the given information, we have two movable pulleys, and the number of supporting ropes is equal to the number of sections of rope between the movable pulleys, which is three. Therefore, the mechanical advantage is:
Mechanical Advantage = 3 * 2 = 6
Since the velocity ratio is given as 5, we know that Mechanical Advantage = Velocity Ratio. So, in this system, the effort moves six times the distance that the load moves. Therefore, the distance moved by the effort is:
Distance moved by the effort = 6 * 40 cm = 240 cm
b) The work done by the effort in lifting the load can be calculated using the formula:
Work = Force * Distance
In this case, the force (effort) is equal to 60N (given), and the distance moved by the effort is 240 cm (calculated in part a). Converting the distance from centimeters to meters:
Distance = 240 cm = 2.4 m
Now, we can calculate the work done:
Work = 60N * 2.4m = 144 J
Therefore, the work done by the effort in lifting the load is 144 Joules.
c) The loss in energy involved in lifting the load can be determined by subtracting the input energy (work done by the effort) from the output energy (potential energy gained by the load).
The potential energy gained by the load can be calculated using the formula:
Potential Energy = Mass * Gravity * Height
Given that the mass of the load is 25kg, the acceleration due to gravity is 9.8 m/s^2, and the height lifted is 0.4 m (40 cm, as given), we can calculate the potential energy gained by the load:
Potential Energy = 25kg * 9.8 m/s^2 * 0.4m = 98 J
Therefore, the loss in energy involved in lifting the load is:
Loss in energy = Potential Energy - Work done by effort = 98 J - 144 J = -46 J (negative indicating the loss in energy)
Hence, the loss in energy involved in lifting the load is 46 Joules.