The arm of a crane at a construction site is
15.0 m long, and it makes an angle of 20.0
◦
with the horizontal. Assume that the maximum load the crane can handle is limited
by the amount of torque the load produces
around the base of the arm.
What maximum torque can the crane withstand if the maximum load the crane can
handle is 799 N?
Answer in units of N · m.

To calculate the maximum torque that the crane can withstand, we can use the formula for torque:

\[
\tau = r \cdot F \cdot \sin(\theta)
\]

Where:
- \(\tau\) is the torque,
- \(r\) is the length of the crane's arm (15.0 m),
- \(F\) is the maximum load force the crane can handle (799 N),
- \(\theta\) is the angle between the arm and the horizontal (20.0°),
- \(\sin(\theta)\) is the sine of the angle.

Let's plug in the values:

\[
\tau = 15.0 \, \text{m} \cdot 799 \, \text{N} \cdot \sin(20.0^\circ)
\]

First, we calculate \(\sin(20.0^\circ)\):
\[
\sin(20.0^\circ) \approx 0.3420
\]

Now substitute that back into the torque equation:
\[
\tau = 15.0 \, \text{m} \cdot 799 \, \text{N} \cdot 0.3420
\]
\[
\tau \approx 4095.99 \, \text{N} \cdot \text{m}
\]

So, the maximum torque the crane can withstand is approximately:

\[
\tau \approx 4096 \, \text{N} \cdot \text{m}
\]

Would you like further details on torque calculation or its applications?

Here are 5 related questions to explore:
1. How does torque depend on the length of the arm in a crane?
2. What happens to the torque if the angle is increased?
3. How does the sine function affect torque in different scenarios?
4. Can the crane handle the same torque if the load is applied at a different angle?
5. How does the direction of the applied force impact torque?

**Tip:** The sine of an angle peaks at 90°, meaning torque is maximized when the force is applied perpendicular to the arm.

The arm of a crane at a construction site is 15.0 m long, and it makes an angle of 20.0° with the horizontal. Assume that the maximum load the crane can handle is limited by the amount of torque the load produces around the base of the arm. What maximum torque can the crane withstand if the maximum load the crane can handle is 799 N? Answer in units of N · m.

Learn how to calculate the maximum torque a crane can withstand when its 15.0m arm makes an angle of 20° with the horizontal, and it carries a load of 799N. This problem involves applying the torque formula, trigonometric functions, and understanding forces, suitable for students in Grades 10-12.

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