Answer
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Step 1:: Understand the problem
We are given that a carabiner has a strength of 24 kN (kilonewtons). We need to find out how much weight the carabiner can hold.
Step 2:: Recall the definition of a newton
A newton (N) is the unit of force. One newton is defined as the force required to accelerate a mass of one kilogram at a rate of one meter per second squared.
Step 3:: Recall the relationship between force and weight
Weight (N) = Mass (kg) imes Acceleration due to gravity (m/s^{2})
Weight is the force exerted on an object due to gravity. The weight of an object is equal to its mass times the acceleration due to gravity. On Earth, the acceleration due to gravity is approximately 9.81 m/s². We can express this relationship as:
Step 4:: Set up the equation to find the maximum weight the carabiner can hold
24,000 N = Mass (kg) imes 9.81 m/s^{2}
To find the maximum weight the carabiner can hold, we set the carabiner's strength (24 kN) equal to the weight and solve for the mass:
Step 5:: Solve for the mass
Mass (kg) = \frac{24,000 N}{9.81 m/s^{2}} \approx 2,446.81 kg
Divide both sides by the acceleration due to gravity (9.81 m/s²) to find the mass:
Step 6:: Convert mass to weight
Weight (N) = 2,446.81 kg imes 9.81 m/s^{2} \approx 23,984.69 N
To find the weight, multiply the mass by the acceleration due to gravity:
Final Answer
A 24 kN carabiner can hold approximately 23,984.69 N (newtons) of weight.
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