A block and tackle has a velocity of 6 and it is being used to raise a mass of 68 newtons through 3 meters. The efficiency is 60%
Calculate the amount of energy needed to lift the mass through 3 meters and calculate the amount of energy that was put into the system
and the loss of energy involved in operating the machine
energy used: mgh=68*3
that assumes it stops at the top (ie has not gained KEnergy).
workin=energyused/.6
energylost in machine=workin*.4
To start, let's calculate the amount of energy needed to lift the mass through 3 meters. The formula for calculating the energy (E) is given by:
E = m * g * h
Where:
E = Energy (in joules)
m = Mass (in kilograms)
g = Acceleration due to gravity (approximately 9.8 m/s^2)
h = Height (in meters)
Given:
Mass (m) = 68 Newtons (1 N = 1 kg)
Height (h) = 3 meters
First, convert the mass from Newtons to kilograms:
1 N = 1 kg, so 68 N = 68 kg
Now substitute the values into the formula:
E = 68 * 9.8 * 3
Calculate:
E = 2004 joules
So, the amount of energy needed to lift the mass through 3 meters is 2004 joules.
Next, let's calculate the amount of energy that was put into the system, taking into account the efficiency. The formula for efficiency (η) is given by:
η = (Useful output energy / Input energy) * 100%
Given:
Efficiency (η) = 60%
We know that the input energy is 2004 joules (calculated previously), and we need to find the useful output energy. Let's represent it as U:
η = (U / 2004) * 100%
Rearrange the formula to solve for U:
U = (η / 100%) * 2004
Substitute the given values:
U = (60 / 100) * 2004
Calculate:
U = 1202.4 joules
So, the amount of energy that was put into the system is approximately 1202.4 joules.
Finally, let's calculate the loss of energy involved in operating the machine by subtracting the useful output energy from the energy needed:
Loss of energy = Energy needed - Useful output energy
Loss of energy = 2004 - 1202.4
Loss of energy = 801.6 joules
Therefore, the loss of energy involved in operating the machine is approximately 801.6 joules.