Hey everyone! I would appreciate it if anyone could help me out with any of this problems! Thanks
1. A cable lifts a 1200 kg elevator at constant velocity for a distance of 35m. What is the work done by:
a) the cable?
b) the weight of the elevator?
the asnwer for a) is 41160 J
the answer for b) is -41160 J
BUTTTTT i dont understand it. I mean, I know the formular is W=Fd. But to find the F, why do you have to multiply 9.8 with the weight? In other words, why do you have to use 9.8? Does it have to do with the constant velocity? Thanks!
1. A cable lifts a 1200 kg elevator at constant velocity for a distance of 35m. What is the work done by:
a) the cable?
b) the weight of the elevator?
the asnwer for a) is 41160 J
the answer for b) is -41160 J
BUTTTTT i dont understand it. I mean, I know the formular is W=Fd. But to find the F, why do you have to multiply 9.8 with the weight? In other words, why do you have to use 9.8? Does it have to do with the constant velocity? Thanks!
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9.8 has to do with gravity, 9.8 m/s^2 is the acceleration due to gravity.
So the mass times the acceleration due to gravity gives you the weight (weight is the force due to gravity, 1200kg is the mass, which is the measurement of how much matter there is, this is an independent characteristic. The weight is that mass times acceleration of gravity**), which is your force.
**F=ma
For the work done by the cable:
You take that weight: 1200kg * 9.8 m/s^2 * the distance (35m) * cos0
(take cos0 because it is moving up, in the direction the cable is lifting it)
The Work for the elevator will be
1200kg * 9.8 m/s^2 * the distance (35m) * cos180
180 because it is doing work in the direction opposite of its movement.
So the mass times the acceleration due to gravity gives you the weight (weight is the force due to gravity, 1200kg is the mass, which is the measurement of how much matter there is, this is an independent characteristic. The weight is that mass times acceleration of gravity**), which is your force.
**F=ma
For the work done by the cable:
You take that weight: 1200kg * 9.8 m/s^2 * the distance (35m) * cos0
(take cos0 because it is moving up, in the direction the cable is lifting it)
The Work for the elevator will be
1200kg * 9.8 m/s^2 * the distance (35m) * cos180
180 because it is doing work in the direction opposite of its movement.
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1200 kg is the mass of the elevator, and to find its weight from its mass that is when you need to multiply by 9.8m/s^2.
Weight is not the same thing as mass. Weight on Earth is a force on a mass due to the acceleration from Earth's gravity. Mass is just how much matter something is made up of. Mass does not change with location; however, weight, or the force of the pull of Earth's gravity does change with location, specifically the location from the center of the Earth. So the acceleration on all objects near Earth's surface is 9.8m/s^2
Since weight is a force and force is calculated by mass x acceleration, then if you take the 1200kg elevator x 9.8m/s^2 you get the force in Newtons instead of pounds. This is equal to 11760 Newtons of force due to the weight of the elevator. So the answer to B, if I understand the question correctly is what is the weight of the elevator, is 11760 Newtons
Now how far did you move the elevator against Earth's Gravity? 35 meters! So to calculate the work done by the force on the cable all you do is take the force x distance moved against the force. +35m x +11760 N = +411600 Nm or +411600 J. Here in this case I called the force pulling up on the elevator as a positive force and the displacement of the elevator as up and that is positive as well.
When the elevator returns to the same floor it started from the work will be -411600 Nm and the network that is done by raising the elevator and lowering it to its original position is 0 Nm.
By the way a Newton meter is a Joule.
Weight is not the same thing as mass. Weight on Earth is a force on a mass due to the acceleration from Earth's gravity. Mass is just how much matter something is made up of. Mass does not change with location; however, weight, or the force of the pull of Earth's gravity does change with location, specifically the location from the center of the Earth. So the acceleration on all objects near Earth's surface is 9.8m/s^2
Since weight is a force and force is calculated by mass x acceleration, then if you take the 1200kg elevator x 9.8m/s^2 you get the force in Newtons instead of pounds. This is equal to 11760 Newtons of force due to the weight of the elevator. So the answer to B, if I understand the question correctly is what is the weight of the elevator, is 11760 Newtons
Now how far did you move the elevator against Earth's Gravity? 35 meters! So to calculate the work done by the force on the cable all you do is take the force x distance moved against the force. +35m x +11760 N = +411600 Nm or +411600 J. Here in this case I called the force pulling up on the elevator as a positive force and the displacement of the elevator as up and that is positive as well.
When the elevator returns to the same floor it started from the work will be -411600 Nm and the network that is done by raising the elevator and lowering it to its original position is 0 Nm.
By the way a Newton meter is a Joule.