Calculating Work Done by the Machine

Oct 13, 2025 by miodeya.com 79 views

If you applied 983 N of force over 6 m into a simple machine to lift a 59 kg box 4 m, what was the efficiency of this simple machine?

To determine the efficiency of the simple machine, we need to calculate the work done by the machine and the work required to lift the box. The work done by the machine is given by the force applied multiplied by the distance over which it is applied. The work required to lift the box is given by the weight of the box multiplied by the height it is lifted.

Calculating Work Done by the Machine

The work done by the machine is given by:

W_{machine} = F \times d

where $F$ is the force applied and $d$ is the distance over which it is applied. In this case, the force applied is 983 N and the distance is 6 m.

W_{machine} = 983 \, \text{N} \times 6 \, \text{m} = 5898 \, \text{J}

Calculating Work Required to Lift the Box

The work required to lift the box is given by:

W_{box} = m \times g \times h

where $m$ is the mass of the box, $g$ is the acceleration due to gravity, and $h$ is the height the box is lifted. In this case, the mass of the box is 59 kg, the acceleration due to gravity is 10 m/s^2, and the height the box is lifted is 4 m.

W_{box} = 59 \, \text{kg} \times 10 \, \text{m/s}^2 \times 4 \, \text{m} = 2360 \, \text{J}

Calculating Efficiency

The efficiency of the machine is given by the ratio of the work done by the machine to the work required to lift the box.

\eta = \frac{W_{machine}}{W_{box}}

Substituting the values calculated earlier, we get:

\eta = \frac{5898 \, \text{J}}{2360 \, \text{J}} = 2.5

Rounding to 1

Rounding the efficiency to 1, we get:

\eta = 2

Therefore, the efficiency of the simple machine is 2.

Conclusion

In this problem, we calculated the efficiency of a simple machine by determining the work done by the machine and the work required to lift a box. We found that the efficiency of the machine is 2, which means that the machine is able to lift the box with 2 times the force applied. This is a measure of the machine's ability to convert the input force into useful work.
Q&A: Understanding the Efficiency of Simple Machines

A: The efficiency of a simple machine is a measure of its ability to convert the input force into useful work. It is calculated by dividing the work done by the machine by the work required to perform the task.

Q: How is the efficiency of a simple machine calculated?

A: The efficiency of a simple machine is calculated by dividing the work done by the machine by the work required to perform the task. The work done by the machine is given by the force applied multiplied by the distance over which it is applied, while the work required to perform the task is given by the weight of the object multiplied by the height it is lifted.

Q: What is the formula for calculating the efficiency of a simple machine?

A: The formula for calculating the efficiency of a simple machine is:

\eta = \frac{W_{machine}}{W_{box}}

where $W_{machine}$ is the work done by the machine and $W_{box}$ is the work required to lift the box.

Q: What is the significance of the efficiency of a simple machine?

A: The efficiency of a simple machine is significant because it determines how effectively the machine can convert the input force into useful work. A machine with high efficiency can perform tasks with less input force, while a machine with low efficiency requires more input force to perform the same task.

Q: Can a simple machine have an efficiency of 100%?

A: No, a simple machine cannot have an efficiency of 100%. This is because there is always some energy lost as heat or friction, which reduces the efficiency of the machine.

Q: What are some common examples of simple machines?

A: Some common examples of simple machines include:

Levers
Pulleys
Inclined planes
Wedges
Screws

Q: How can the efficiency of a simple machine be improved?

A: The efficiency of a simple machine can be improved by:

Reducing friction and heat loss
Increasing the mechanical advantage of the machine
Using materials with high strength-to-weight ratios
Optimizing the design of the machine

Q: What are some real-world applications of simple machines?

A: Simple machines have many real-world applications, including:

Construction equipment
Manufacturing machinery
Automotive systems
Aerospace engineering

Conclusion

In this Q&A article, we have discussed the efficiency of simple machines and how it is calculated. We have also explored the significance of efficiency and how it can be improved. By understanding the efficiency of simple machines, we can design and build more effective machines that can perform tasks with less input force.