https://file.aiquickdraw.com/mathbot/file/1727172769277xtjxi3zq.jpg

Miley Cyrus spots a wrecking ball of mass MM = 80.0 [kg]  that is suspended by two strings as shown. She wants to cut string BB so that she can swing on it. What is the tension on the string that she's about to cut? use g= 9.81 m/s^2

In this problem, we need to calculate the tension in string \( B \) before it is cut. This involves resolving forces and applying equilibrium conditions since the wrecking ball is at rest.

### Step-by-step solution:

1. **Weight of the wrecking ball:**
   The weight of the wrecking ball \( M = 80 \, \text{kg} \) is given by:
   \[
   W = M \cdot g = 80 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 784.8 \, \text{N}
   \]

2. **Equilibrium conditions:**
   Since the system is in equilibrium, the sum of forces in both the horizontal and vertical directions must be zero.

   - In the vertical direction:
     \[
     T_A \sin(30^\circ) + T_B \sin(45^\circ) = W
     \]
   - In the horizontal direction:
     \[
     T_A \cos(30^\circ) = T_B \cos(45^\circ)
     \]

   Where:
   - \( T_A \) is the tension in string \( A \),
   - \( T_B \) is the tension in string \( B \),
   - \( W \) is the weight of the ball.

3. **Solve the system of equations:**

   From the horizontal equilibrium equation:
   \[
   T_A = T_B \frac{\cos(45^\circ)}{\cos(30^\circ)}
   \]
   Substituting numerical values for the cosines:
   \[
   T_A = T_B \frac{0.7071}{0.8660} = 0.8165 T_B
   \]

   Now, substitute \( T_A = 0.8165 T_B \) into the vertical equilibrium equation:
   \[
   0.8165 T_B \sin(30^\circ) + T_B \sin(45^\circ) = 784.8 \, \text{N}
   \]
   Substituting the values for the sines:
   \[
   0.8165 T_B \times 0.5 + T_B \times 0.7071 = 784.8 \, \text{N}
   \]
   Simplifying:
   \[
   0.40825 T_B + 0.7071 T_B = 784.8
   \]
   \[
   1.11535 T_B = 784.8
   \]
   Solving for \( T_B \):
   \[
   T_B = \frac{784.8}{1.11535} = 703.7 \, \text{N}
   \]

### Conclusion:
The tension in string \( B \) is approximately \( 703.7 \, \text{N} \).

Would you like more details on any step?

---

Here are 5 related questions to explore further:

1. How would the tensions change if the mass of the wrecking ball were increased?
2. What would happen to the tension in string \( A \) if string \( B \) were cut?
3. How can we determine the maximum tension each string can withstand before breaking?
4. What role do the angles of the strings play in distributing the forces?
5. How would the system change if the angles \( A \) and \( B \) were both equal?

**Tip:** Always resolve forces into horizontal and vertical components when dealing with equilibrium problems.

Miley Cyrus spots a wrecking ball of mass M = 80.0 [kg] that is suspended by two strings as shown. She wants to cut string B so that she can swing on it. What is the tension on the string that she's about to cut? Use g= 9.81 m/s^2

Calculate the tension in string B before Miley Cyrus cuts it to swing on a wrecking ball of mass 80 kg. This problem involves using equilibrium conditions and resolving forces. Ideal for students learning about statics, equilibrium, and tension forces.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation