Question

a boy pulls his toy on a smooth horizontal surface with a rope inclined at 60° to the horizontal if the effective Force pulling the toy along the horizontal surface is 5-newton calculate the tension in the rope

Answer 1

The tension in the rope is 10 N

Step-by-step explanation:

The Force Vector

Like all vectors, the force has a magnitude and direction. Vectors can be decomposed into two perpendicular components on both axes.

The tension in the rope (F) can be calculated by using vector decomposition as follows.

The figure included below shows a force F which horizontal component is known to have a value of Fx= 5 Nw. The angle formed by the force and its horizontal component is 60°.

We can use the trigonometric ratio called the cosine to find the magnitude of F as follows:

`\displaystyle \cos 60^\circ = (5)/(F)`

Solving for F:

`\displaystyle F = (5)/(\cos 60^\circ)`

`\displaystyle F = (5)/((1)/(2))`

Thus, F = 10 N

The tension in the rope is 10 N