Question

1. a boy pulls a cart with a force of 6 n east, while another boy pulls with a force of 8 n making an angle of 90° with the first force. use the parallelogram law to determine the resultant force.

Explanation:

Step1: Identify the forces and the angle

We have two forces $F_1 = 6\ N$ and $F_2=8\ N$, and the angle between them $\theta = 90^{\circ}$.

Step2: Apply the parallelogram - law formula

The magnitude of the resultant force $R$ of two forces $F_1$ and $F_2$ with an angle $\theta$ between them is given by $R=\sqrt{F_1^{2}+F_2^{2}+2F_1F_2\cos\theta}$. Since $\theta = 90^{\circ}$ and $\cos90^{\circ}=0$, the formula simplifies to $R=\sqrt{F_1^{2}+F_2^{2}}$.
Substitute $F_1 = 6\ N$ and $F_2 = 8\ N$ into the formula: $R=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}$.

Step3: Calculate the value of the resultant force

$\sqrt{100}=10\ N$.

Answer:

$10\ N$