A boy is pulling his toy on a smooth horizontal surface with a rope inclined at 60° to the horizontal . if the effective force is pulling the toy along the horizontal surface is 5newton , calculate the tension . show full working
To calculate the tension in the rope, we can break down the force into its horizontal and vertical components.
1. Determine the horizontal and vertical components of the force:
Given that the force is pulling the toy along the horizontal surface, the horizontal component of the force will be equal to the effective force, which is 5 Newtons. The vertical component can be found by using trigonometry. The vertical force component can be calculated using the formula:
Vertical component = Effective force * sin(θ)
θ = 60°
So, the vertical component of the force = 5 N * sin(60°) = 5 N * 0.866 = 4.33 N (approx)
2. Calculate the tension in the rope:
The tension in the rope will be equal to the vector sum of the horizontal and vertical components. Since the horizontal component doesn't contribute to the tension, the tension in the rope will be equal to the vertical component of the force:
Tension = Vertical component of force = 4.33 N
Therefore, the tension in the rope is approximately 4.33 Newtons.