Child weighs 29 kg on a swing supported by two chains. Another child pulls swing back to the chains to make 30 degree angle with the vertical. What force is exerted by each chain
well, mg is downward, so tension must be
sin30=mg/tension solve for tension.
To determine the force exerted by each chain on the swing, we can break down the gravitational force into its vertical and horizontal components.
First, let's find the weight of the child on the swing. Given that the child weighs 29 kg, we can use the formula:
Weight = mass * acceleration due to gravity
Weight = 29 kg * 9.8 m/s^2
Weight = 284.2 N
Now, let's analyze the forces acting on the swing when it is at a 30-degree angle with the vertical. The weight of the child can be broken down into two components: the force acting vertically downward (F_vertical) and the force acting horizontally (F_horizontal).
The force acting vertically downward (F_vertical) can be calculated using trigonometry. We can use the formula:
F_vertical = Weight * cos(angle)
F_vertical = 284.2 N * cos(30°)
F_vertical = 284.2 N * 0.866 (rounded to three decimal places)
F_vertical ≈ 246.373 N
The force acting horizontally (F_horizontal) can also be calculated using trigonometry. We can use the formula:
F_horizontal = Weight * sin(angle)
F_horizontal = 284.2 N * sin(30°)
F_horizontal = 284.2 N * 0.5
F_horizontal ≈ 142.1 N
Since the swing is supported by two chains, each chain will exert an equal amount of force. Therefore, the force exerted by each chain is half of the total vertical force.
Force exerted by each chain = F_vertical / 2
Force exerted by each chain = 246.373 N / 2
Force exerted by each chain ≈ 123.187 N
So, the force exerted by each chain on the swing is approximately 123.187 Newtons.