Two forces acting on an object have magnitudes of 22 N and 14 N and directions that differ by 50 degrees. Determine the magnitude of the product of mass and acceleration for the body. Give your answer in units of kgms-2, accurate to the nearest integer (whole number).


Hint: first draw a vector diagram for forces you are adding aligned to a sensible x and y axis. Add orthogonal components, then find the magnitude of the resultant.

To solve this problem, we'll use vector addition to determine the resultant force on the object. Then, since \( F = ma \), the magnitude of the resultant force will also be equal to the product of mass and acceleration, which we need to find.

### Steps:

1. **Break the forces into components**:
   We'll align one force along the \(x\)-axis and then break the other into components along the \(x\)- and \(y\)-axes.

   - Let \( F_1 = 22 \, \text{N} \) act along the \(x\)-axis.
   - Let \( F_2 = 14 \, \text{N} \) act at an angle of 50° to \( F_1 \).

   The components of \( F_2 \) are:
   - \( F_{2x} = F_2 \cos(50^\circ) \)
   - \( F_{2y} = F_2 \sin(50^\circ) \)

2. **Find the total force components**:
   The total force in the \(x\)-direction and \(y\)-direction can be calculated as follows:
   - \( F_x = F_1 + F_{2x} = 22 + 14 \cos(50^\circ) \)
   - \( F_y = F_{2y} = 14 \sin(50^\circ) \)

3. **Find the magnitude of the resultant force**:
   The magnitude of the resultant force \( F_{\text{resultant}} \) is given by:
   \[
   F_{\text{resultant}} = \sqrt{F_x^2 + F_y^2}
   \]

4. **Calculate the value**:
   Let’s compute the components and find the resultant magnitude.The magnitude of the product of mass and acceleration (which is equal to the resultant force) is approximately \( 33 \, \text{kg} \, \text{m/s}^2 \) (rounded to the nearest integer).

Would you like more details on any part of this calculation?

Here are 5 related questions to deepen your understanding:

1. How would the magnitude of the resultant force change if the angle between the forces increased?
2. What happens to the resultant force if the magnitudes of both forces are doubled?
3. How do the \(x\)- and \(y\)-components of a vector help in understanding vector addition?
4. If the forces were perpendicular (i.e., 90 degrees apart), how would the magnitude of the resultant force change?
5. How is this vector addition applicable in real-world problems involving forces?

**Tip:** When working with forces, always resolve them into components along perpendicular axes, as it simplifies vector addition greatly.

Two forces acting on an object have magnitudes of 22 N and 14 N and directions that differ by 50 degrees. Determine the magnitude of the product of mass and acceleration for the body. Give your answer in units of kgms-2, accurate to the nearest integer (whole number).

Learn how to calculate the magnitude of the resultant force when two forces act at an angle of 50 degrees, with magnitudes of 22 N and 14 N. This solution involves vector addition, trigonometric functions, and Newton's Second Law. Suitable for high school students in Grades 9-12.

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