The two angled ropes used to support the crate in Figure P5.7 can withstand a maximum tension of 1500 N before they break. What is the largest mass the ropes can support?
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To find the largest mass that the ropes can support, we need to consider the tension in the ropes. The tension in a rope is equal to the weight it is supporting.
Let's assume that the crate is hanging freely from the two angled ropes. In this case, the tension in each rope will be half the weight of the crate, since each rope supports an equal share of the weight.
The maximum tension that each rope can withstand is given as 1500 N. Therefore, the maximum tension in each rope should not exceed that value.
Since the tension in each rope is equal to half the weight of the crate, we can set up the following equation:
Tension (in each rope) = Weight (of the crate) / 2
1500 N = Weight (of the crate) / 2
Now, we can solve this equation to find the weight (mass) of the crate:
Weight (of the crate) = 1500 N * 2
Weight (of the crate) = 3000 N
To find the mass, we need to convert the weight from Newtons to kilograms. We can use the equation:
Weight (in kilograms) = Weight (in Newtons) / gravitational acceleration
The gravitational acceleration is approximately 9.8 m/s².
Weight (in kilograms) = 3000 N / 9.8 m/s²
Weight (in kilograms) ≈ 306.12 kg
Therefore, the largest mass the ropes can support is approximately 306.12 kg.