- A 1600-KG ELEVATOR accelerates downward at 2.00 m/s2 starting from rest. how much work does gravity do on the elevator? b) how much does tention in the elevator cable do on the elevator? c) use the work kinetic energy theorem to find the kenetic energy of the elevator as it reaches 20 meter. c)what is the sped of the elevator as it reaches 20 meter.
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To find the answers to these questions, we need to use some basic principles of physics. Let's go step by step:
a) How much work does gravity do on the elevator?
The work done by gravity can be calculated using the formula: Work = Force × Distance × cos(angle)
In this case, the force due to gravity is the weight of the elevator, which is given by the equation: Weight = mass × acceleration due to gravity
So, the work done by gravity on the elevator is given by: Work = Weight × Distance × cos(180°) because the elevator is moving downward.
Plugging in the values: Weight = mass × acceleration due to gravity = 1600 kg × 9.8 m/s^2 (acceleration due to gravity on Earth).
Distance is not provided in the question, so we cannot calculate the work done by gravity without this information.
b) How much tension in the elevator cable does on the elevator?
Since the elevator is accelerating downward, the tension in the cable will be greater than the weight of the elevator. The net force acting on the elevator is given by the equation: Net Force = mass × acceleration.
So, the tension in the elevator cable can be calculated by adding the force due to gravity (mg) and the net force (ma): Tension = Weight + Net Force.
Plugging in the values: Weight = mass × acceleration due to gravity = 1600 kg × 9.8 m/s^2 (acceleration due to gravity on Earth).
The net force can be calculated using the equation: Net Force = mass × acceleration.
c) Use the work-energy theorem to find the kinetic energy of the elevator as it reaches 20 meters.
The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
The work done on the elevator can be calculated using the formula: Work = Force × Distance.
In this case, the force is the net force acting on the elevator, which is the sum of the force due to gravity and the tension in the cable:
Net Force = Weight + Tension.
The work done by this net force will be equal to the change in kinetic energy of the elevator:
Work = ΔKE (change in kinetic energy).
So, using the equation: Work = ΔKE, we can find the change in kinetic energy of the elevator.
c) What is the speed of the elevator as it reaches 20 meters?
To find the speed of the elevator at a given position, we can use the principle of conservation of mechanical energy.
The initial mechanical energy (at rest) of the elevator is equal to the final mechanical energy (at 20 meters).
The initial mechanical energy is given by the equation: E_initial = PE_initial + KE_initial.
Since the elevator is at rest, the initial potential energy (PE_initial) is equal to the initial kinetic energy (KE_initial) = 0.
The final mechanical energy is given by the equation: E_final = PE_final + KE_final.
At 20 meters, the potential energy (PE_final) is equal to the weight of the elevator times the height (PE_final = Weight × height).
Since we have the change in kinetic energy (ΔKE) from the previous question, we can calculate the final kinetic energy (KE_final) using the equation: ΔKE = KE_final - KE_initial.
Once we have the final kinetic energy, we can use the kinetic energy equation: KE = 0.5 × mass × velocity^2 to solve for the speed of the elevator (velocity) at 20 meters.