Question

A box is resting on the ground and you can assume its location is the origin of the system. A person applies a westward force of 31.7 Newtons (N) to the box while another applies a northward force of 43.5 N to the box. Determine the total force applied to the box.

Answer 1

Answer on Question #61586 - Physics - Mechanics | Relativity

Question:

A box is resting on the ground and you can assume its location is the origin of the system. A person applies a westward force of 31.7 Newtons (N) to the box while another applies a northward force of $43.5\mathrm{N}$ to the box. Determine the total force applied to the box.

Answer:

The total force $\overrightarrow{F_T}$ is the sum of force applies a westward and of force applied a northward:

$$\overrightarrow {F _ {T}} = \overrightarrow {F _ {W}} + \overrightarrow {F _ {N}}$$

Absolute value of $\overrightarrow{F_T}$ is:

$$F _ {T} = \sqrt {F _ {W} ^ {2} + F _ {N} ^ {2}}$$ $$F _ {T} = \sqrt {3 1 . 7 ^ {2} + 4 3 . 5 ^ {2}} \approx 5 3. 8 3 (N)$$

The total force applied to the box is 53.83 N.

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