Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
Answer:
To find the efficiency of the screw jack, we first need to determine the ideal mechanical advantage (IMA) and then use it to calculate efficiency.
Given:
- Pitch of the screw jack (p) = 0.5 cm
- Length of the arm (lever arm) of the screw jack (L) = 50 cm
- Mechanical advantage (MA) = 200
The ideal mechanical advantage (IMA) of the screw jack is calculated using the formula:
\[ \text{IMA} = \frac{\text{Length of travel}}{\text{Pitch}} \]
For one complete turn of the screw (which raises the jack by one pitch):
\[ \text{Length of travel} = 2 \pi \cdot \text{Lever arm} = 2 \pi \cdot 50 \text{ cm} = 100 \pi \text{ cm} \]
Therefore,
\[ \text{IMA} = \frac{100 \pi \text{ cm}}{0.5 \text{ cm}} = 200 \pi \]
Now, efficiency (η) is given by the formula:
\[ \eta = \frac{\text{MA}}{\text{IMA}} \times 100\% \]
Substitute the given values:
\[ \eta = \frac{200}{200 \pi} \times 100\% \]
\[ \eta = \frac{1}{\pi} \times 100\% \]
\[ \eta = \frac{100}{\pi}\% \]
Therefore, the efficiency of the screw jack is:
\[ \boxed{\frac{100}{\pi}\%} \]
This is the exact expression for the efficiency of the machine in terms of \( \pi \).
Explanation:
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.
