A 3.00 watt electric motor is plugged into an electrical outlet. It takes the motor 30.00 seconds to lift a mass of 254.9 g a distance of 10.00 cm. In that time, the motor has used 90.00 J of energy. Assuming no energy leaves the system, how much heat has been added to the system by the end of those 30 seconds?
power = work/time, so
work = power*time = 3.00*30.00 = 90.00 J
but the actual work done was only
work = Fd = 0.2549*9.8*0.10 = 0.2498J
so, what do you think?
To find the amount of heat added to the system by the end of 30 seconds, we need to first calculate the work done by the motor, and then subtract that from the total energy used by the motor.
1. Calculate the work done by the motor:
The work done by the motor can be calculated using the formula:
Work = Force x Distance
Since the work is done in lifting the mass, the force can be calculated using the formula:
Force = Mass x Gravity
The gravitational force can be calculated using the formula:
Gravity = Mass x Acceleration due to Gravity
Plugging in the values:
Mass = 254.9 g = 0.2549 kg
Acceleration due to Gravity = 9.8 m/s^2
Gravity = 0.2549 kg x 9.8 m/s^2 = 2.49902 N
The distance is given as 10.00 cm, which needs to be converted to meters:
Distance = 10.00 cm = 0.10 m
Now we can calculate the work done:
Work = 2.49902 N x 0.10 m = 0.249902 J
2. Find the heat added to the system:
Heat = Total Energy Used - Work
The given total energy used is 90.00 J, and the work done is 0.249902 J.
Heat = 90.00 J - 0.249902 J = 89.750098 J
Therefore, by the end of those 30 seconds, the motor has added 89.750098 J of heat to the system.
To find out how much heat has been added to the system, we need to calculate the efficiency of the electric motor first.
The formula for efficiency is:
Efficiency = Useful output energy / Total input energy
In this case, useful output energy is the work done by the motor in lifting the mass, and total input energy is the electrical energy consumed by the motor.
First, let's calculate the work done by the motor in lifting the mass. The work done is given by the formula:
Work = Force × Distance
The force can be calculated using Newton's second law of motion:
Force = mass × acceleration
Acceleration can be determined using the kinematic equation:
Distance = (1/2) × acceleration × time^2
Rearranging the equation, we can solve for acceleration:
acceleration = (2 × Distance) / (time^2)
Substituting the given values:
acceleration = (2 × 0.1 m) / (30 s)^2
acceleration ≈ 0.0222 m/s^2
Now, we can calculate the force:
Force = mass × acceleration
Force = 0.2549 kg × 0.0222 m/s^2
Force ≈ 0.0057 N
Next, let's calculate the useful output energy, which is equal to the work done:
Useful output energy = Work = Force × Distance
Useful output energy = 0.0057 N × 0.1 m
Useful output energy = 0.00057 J
Now, let's calculate the efficiency of the electric motor:
Efficiency = Useful output energy / Total input energy
Efficiency = 0.00057 J / 90 J
Efficiency ≈ 0.0063
The efficiency of the motor is approximately 0.0063, or 0.63%.
Since no energy leaves the system, the amount of heat added to the system would be the same as the total input energy:
Heat added to the system = Total input energy = 90 J
Therefore, by the end of those 30 seconds, the amount of heat added to the system is 90 J.
the lifted mass gains potential energy ... m * g * h
... .2549 kg * 9.8 m/s^2 * .01000 m = ?
the rest of the 90.00 J consumed by the motor becomes "waste" heat