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A differential wheel and axle is used to lift a box of mass 4000 kg. The larger and smaller radii of the beam are 40 cm and 30 cm respectively. The length of the crank arm is 50 cm . If the efficiency of the machine is 80 per cent, determine the motive force required to lift the load, the velocity ratio and the mechanical advantage gained.?
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A differential wheel and axle is used to lift a box of mass 4000 kg. T...
Differential Wheel and Axle
The differential wheel and axle is a simple machine that consists of a wheel with two different radii connected by a beam. It is used to lift heavy loads with less effort by taking advantage of the mechanical advantage gained through the use of different radii.
Given Information:
- Mass of the box (load): 4000 kg
- Larger radius of the beam: 40 cm
- Smaller radius of the beam: 30 cm
- Length of the crank arm: 50 cm
- Efficiency of the machine: 80%
Motive Force Required to Lift the Load:
The motive force required to lift the load can be determined using the equation:
Motive force = Load × Mechanical Advantage
Since the efficiency of the machine is given, we need to calculate the mechanical advantage first.
Mechanical Advantage:
The mechanical advantage of the differential wheel and axle can be calculated using the formula:
Mechanical Advantage = Radius of the larger wheel / Radius of the smaller wheel
Substituting the given values:
Mechanical Advantage = 40 cm / 30 cm = 4/3
Now we can calculate the motive force:
Motive force = 4000 kg × (4/3) = 5333.33 N
Therefore, the motive force required to lift the load is 5333.33 N.
Velocity Ratio:
The velocity ratio of the differential wheel and axle can be calculated using the formula:
Velocity Ratio = Distance moved by the effort / Distance moved by the load
In this case, the distance moved by the effort is equal to the circumference of the crank arm, which is 2π × 50 cm, and the distance moved by the load is equal to the circumference of the larger wheel, which is 2π × 40 cm.
Velocity Ratio = (2π × 50 cm) / (2π × 40 cm) = 5/4
Therefore, the velocity ratio of the machine is 5/4.
Mechanical Advantage Gained:
The mechanical advantage gained by using the differential wheel and axle can be calculated using the formula:
Mechanical Advantage Gained = Velocity Ratio / Efficiency
Substituting the given values:
Mechanical Advantage Gained = (5/4) / 0.8 = 1.25
Therefore, the mechanical advantage gained by using the machine is 1.25.
To summarize:
- The motive force required to lift the load is 5333.33 N.
- The velocity ratio of the machine is 5/4.
- The mechanical advantage gained by using the machine is 1.25.
The differential wheel and axle is a simple machine that consists of a wheel with two different radii connected by a beam. It is used to lift heavy loads with less effort by taking advantage of the mechanical advantage gained through the use of different radii.
Given Information:
- Mass of the box (load): 4000 kg
- Larger radius of the beam: 40 cm
- Smaller radius of the beam: 30 cm
- Length of the crank arm: 50 cm
- Efficiency of the machine: 80%
Motive Force Required to Lift the Load:
The motive force required to lift the load can be determined using the equation:
Motive force = Load × Mechanical Advantage
Since the efficiency of the machine is given, we need to calculate the mechanical advantage first.
Mechanical Advantage:
The mechanical advantage of the differential wheel and axle can be calculated using the formula:
Mechanical Advantage = Radius of the larger wheel / Radius of the smaller wheel
Substituting the given values:
Mechanical Advantage = 40 cm / 30 cm = 4/3
Now we can calculate the motive force:
Motive force = 4000 kg × (4/3) = 5333.33 N
Therefore, the motive force required to lift the load is 5333.33 N.
Velocity Ratio:
The velocity ratio of the differential wheel and axle can be calculated using the formula:
Velocity Ratio = Distance moved by the effort / Distance moved by the load
In this case, the distance moved by the effort is equal to the circumference of the crank arm, which is 2π × 50 cm, and the distance moved by the load is equal to the circumference of the larger wheel, which is 2π × 40 cm.
Velocity Ratio = (2π × 50 cm) / (2π × 40 cm) = 5/4
Therefore, the velocity ratio of the machine is 5/4.
Mechanical Advantage Gained:
The mechanical advantage gained by using the differential wheel and axle can be calculated using the formula:
Mechanical Advantage Gained = Velocity Ratio / Efficiency
Substituting the given values:
Mechanical Advantage Gained = (5/4) / 0.8 = 1.25
Therefore, the mechanical advantage gained by using the machine is 1.25.
To summarize:
- The motive force required to lift the load is 5333.33 N.
- The velocity ratio of the machine is 5/4.
- The mechanical advantage gained by using the machine is 1.25.
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A differential wheel and axle is used to lift a box of mass 4000 kg. The larger and smaller radii of the beam are 40 cm and 30 cm respectively. The length of the crank arm is 50 cm . If the efficiency of the machine is 80 per cent, determine the motive force required to lift the load, the velocity ratio and the mechanical advantage gained.?
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A differential wheel and axle is used to lift a box of mass 4000 kg. The larger and smaller radii of the beam are 40 cm and 30 cm respectively. The length of the crank arm is 50 cm . If the efficiency of the machine is 80 per cent, determine the motive force required to lift the load, the velocity ratio and the mechanical advantage gained.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A differential wheel and axle is used to lift a box of mass 4000 kg. The larger and smaller radii of the beam are 40 cm and 30 cm respectively. The length of the crank arm is 50 cm . If the efficiency of the machine is 80 per cent, determine the motive force required to lift the load, the velocity ratio and the mechanical advantage gained.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A differential wheel and axle is used to lift a box of mass 4000 kg. The larger and smaller radii of the beam are 40 cm and 30 cm respectively. The length of the crank arm is 50 cm . If the efficiency of the machine is 80 per cent, determine the motive force required to lift the load, the velocity ratio and the mechanical advantage gained.?.
A differential wheel and axle is used to lift a box of mass 4000 kg. The larger and smaller radii of the beam are 40 cm and 30 cm respectively. The length of the crank arm is 50 cm . If the efficiency of the machine is 80 per cent, determine the motive force required to lift the load, the velocity ratio and the mechanical advantage gained.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A differential wheel and axle is used to lift a box of mass 4000 kg. The larger and smaller radii of the beam are 40 cm and 30 cm respectively. The length of the crank arm is 50 cm . If the efficiency of the machine is 80 per cent, determine the motive force required to lift the load, the velocity ratio and the mechanical advantage gained.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A differential wheel and axle is used to lift a box of mass 4000 kg. The larger and smaller radii of the beam are 40 cm and 30 cm respectively. The length of the crank arm is 50 cm . If the efficiency of the machine is 80 per cent, determine the motive force required to lift the load, the velocity ratio and the mechanical advantage gained.?.
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A differential wheel and axle is used to lift a box of mass 4000 kg. The larger and smaller radii of the beam are 40 cm and 30 cm respectively. The length of the crank arm is 50 cm . If the efficiency of the machine is 80 per cent, determine the motive force required to lift the load, the velocity ratio and the mechanical advantage gained.?, a detailed solution for A differential wheel and axle is used to lift a box of mass 4000 kg. The larger and smaller radii of the beam are 40 cm and 30 cm respectively. The length of the crank arm is 50 cm . If the efficiency of the machine is 80 per cent, determine the motive force required to lift the load, the velocity ratio and the mechanical advantage gained.? has been provided alongside types of A differential wheel and axle is used to lift a box of mass 4000 kg. The larger and smaller radii of the beam are 40 cm and 30 cm respectively. The length of the crank arm is 50 cm . If the efficiency of the machine is 80 per cent, determine the motive force required to lift the load, the velocity ratio and the mechanical advantage gained.? theory, EduRev gives you an
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