A 200 kg piano is suspended by a rope from a high building. (Assume the mass of the rope is zero).
a. What is the weight of the piano?
b. What is the tension of the rope?
c. The piano is now hoisted up with an initial acceleration of 1 m/s. What is the minimum value of the breaking stain of a rope capable of supporting the piano now?
To answer these questions, we need to understand a few concepts related to forces. Let's break it down step by step.
a. What is the weight of the piano?
The weight of an object can be calculated using the formula: weight = mass x acceleration due to gravity (g). In this case, the mass of the piano is given as 200 kg.
To find the acceleration due to gravity, we need to know the value. On Earth, the approximate value of acceleration due to gravity is 9.8 m/s².
So, to find the weight of the piano, we calculate: weight = 200 kg x 9.8 m/s².
b. What is the tension of the rope?
The tension in the rope is equal to the weight of the piano. This is because the rope is supporting the weight of the piano, so the tension in the rope will be equal to the force exerted by the weight.
Therefore, the tension in the rope is also 200 kg x 9.8 m/s².
c. What is the minimum value of the breaking strain of a rope capable of supporting the piano now?
To calculate the minimum value of the breaking strain of the rope, we need to consider the acceleration of the piano.
The formula to calculate the tension in the rope with acceleration is: tension = mass x (acceleration + gravity).
In this case, we know the mass of the piano is 200 kg, and the acceleration is given as 1 m/s².
So, the tension in the rope with acceleration will be: tension = 200 kg x (1 m/s² + 9.8 m/s²).
Now, the "breaking strain" refers to the maximum force a material can withstand before breaking or failing. In this case, the breaking strain of the rope should be greater than or equal to the tension calculated in the previous step.
Therefore, the minimum value of the breaking strain of the rope capable of supporting the piano now is the tension calculated above, which is 200 kg x (1 m/s² + 9.8 m/s²).