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The problem involves a stationary ball with a mass of 20 kg hanging on a string, being pulled by a force \( F \) at an angle of 35° to the horizontal.

To determine the size of the force \( F \), let's break it down:

### Given:
- Mass \( m = 20 \, \text{kg} \)
- Angle \( \theta = 35^\circ \)
- Gravitational acceleration \( g = 9.8 \, \text{m/s}^2 \)

### Step 1: Calculate the weight of the ball
The weight of the ball is the force due to gravity:
\[
W = m \cdot g = 20 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 196 \, \text{N}
\]
This weight acts vertically downward.

### Step 2: Resolve forces
Since the ball is stationary, the tension in the string must balance both the vertical and horizontal forces. The force \( F \) is applied at an angle of 35°, so we can resolve \( F \) into its vertical and horizontal components:
- Vertical component: \( F_{\text{vertical}} = F \cdot \sin(\theta) \)
- Horizontal component: \( F_{\text{horizontal}} = F \cdot \cos(\theta) \)

For equilibrium in the vertical direction, the vertical component of the force \( F \) must balance the weight of the ball:
\[
F \cdot \sin(35^\circ) = 196 \, \text{N}
\]

### Step 3: Solve for \( F \)
\[
F = \frac{196}{\sin(35^\circ)}
\]

Let me calculate that.The magnitude of the force \( F \) pulling on the mass of the ball is approximately \( 341.7 \, \text{N} \).

It seems none of the options provided matches this result exactly, which could suggest either a misunderstanding in interpretation or a misprint in the options.

Do you need further details or clarifications?

Here are five related questions to deepen your understanding:
1. How would the required force \( F \) change if the angle were increased?
2. What happens to the vertical and horizontal components of \( F \) as the angle approaches 90°?
3. How is the horizontal component of \( F \) relevant in this scenario?
4. What assumptions are made about the string in this problem?
5. How would the solution change if the ball were in motion instead of stationary?

**Tip:** Always remember that angles in force problems are crucial, as they affect both the magnitude and direction of the forces involved.

A stationary ball with a mass of 20 kg is placed on a string and is pulled by a force, F, angled at 35°. What is the size of the force, F, pulling on the mass of the ball?

Learn how to calculate the force pulling a 20 kg stationary ball at a 35° angle using trigonometry and equilibrium principles. This detailed problem solution includes force decomposition and equilibrium analysis. Suitable for students in Grades 10-12.

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