Calculate the tension in the string if a single pulley of velocity ratio 5 is used to raise a body of mass 200g through a distance of 4cm.
To calculate the tension in the string, we need to consider the principles of work and energy. The work done on the body is given by the formula:
Work = Force × Distance × Velocity Ratio
First, let's convert the mass from grams to kilograms:
Mass = 200g = 0.2kg
Next, we need to calculate the work done on the body. We are given the distance and the velocity ratio, so we can substitute those values into the formula:
Work = Force × Distance × Velocity Ratio
Work = Tension × Distance × Velocity Ratio
Work = Tension × 0.04m × 5
Now, we know that work done on the body is equal to the change in potential energy of the body. The potential energy is given by the formula:
Potential Energy = Mass × Acceleration due to gravity × Height
Let's substitute the known values into this equation:
Potential Energy = 0.2kg × 9.8m/s^2 × 0.04m
The work done by the tension is equal to the change in potential energy, so we set the two equations equal to each other:
Tension × 0.04m × 5 = 0.2kg × 9.8m/s^2 × 0.04m
Now we can solve for the tension:
Tension = (0.2kg × 9.8m/s^2 × 0.04m) / (0.04m × 5)
Tension = 0.2kg × 9.8m/s^2 / 5
Tension = 0.392N
Therefore, the tension in the string is 0.392 Newtons.