How Is the Elevator's Acceleration Calculated Using Newton's Second Law?

Therefore, Fge = 1000kg * 9.8m/s^2 = 9800N. Using the equation FNET=ma, we can set up the following equation:FNET = 2(6000N) - 9800N = 1000kg * aSolving for a, we get:a = (12000N - 9800N) / 1000kg = 2200N / 1000kg = 2.2m/s^2In summary, the acceleration of the elevator is 2.2m/s^2 and the force of gravity exerted on the elevator is 9800N. This was found using the formula FNET=
  • #1
cheerspens
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Homework Statement



A 1000 kg elevator is held up by two cables. If each able exerts a force of 6000N upwards upon the elevator, find the elevator's acceleration.

Homework Equations



Fg=mg

FNET=ma

The Attempt at a Solution



I started with a force diagram to help me and then I think I'm supposed to use the FNET=ma formula. So I plugged in the variables as follows: (6000+6000)-Fge=1000a
How do you solve for acceleration in this problem when I also need to find the Force that gravity exerts on the elevator (Fge)?

Would the answer be 2.2m/s^2?
 
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  • #2
Fge would simply be the weight, mg, of the elevator.
 
  • #3


Yes, you are on the right track. In order to solve for the elevator's acceleration, you will need to use both Newton's 2nd Law (FNET = ma) and the equation for gravitational force (Fg = mg).

First, let's find the force of gravity acting on the elevator. We know that the mass of the elevator is 1000 kg, so we can plug that into the equation Fg = mg. This gives us Fg = (1000 kg)(9.8 m/s^2) = 9800 N.

Now, we can use this value for Fg in the FNET = ma equation. We know that the net force acting on the elevator is the sum of the upward forces (6000 N + 6000 N) minus the force of gravity (9800 N). This gives us:

FNET = (6000 N + 6000 N) - 9800 N = 2200 N

Now, we can plug this value for FNET into the FNET = ma equation to solve for the acceleration (a):

2200 N = (1000 kg)a

a = 2200 N / 1000 kg = 2.2 m/s^2

So, the elevator's acceleration is 2.2 m/s^2.
 

FAQ: How Is the Elevator's Acceleration Calculated Using Newton's Second Law?

What is Newton's 2nd Law of Motion?

Newton's 2nd Law of Motion states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. This means that the greater the force applied to an object, the greater its acceleration will be. However, the greater the mass of an object, the smaller its acceleration will be for the same amount of force.

How is Newton's 2nd Law expressed mathematically?

The mathematical expression of Newton's 2nd Law is F=ma, where F is the net force applied to the object, m is the mass of the object, and a is the resulting acceleration of the object. This equation shows that the acceleration of an object is directly proportional to the net force applied and inversely proportional to its mass.

Can Newton's 2nd Law be applied to both linear and rotational motion?

Yes, Newton's 2nd Law can be applied to both linear and rotational motion. In linear motion, the force and acceleration are in the same direction, while in rotational motion, the force and acceleration are perpendicular to each other. However, the same principle applies - the greater the force applied, the greater the resulting acceleration will be.

What is the difference between mass and weight in relation to Newton's 2nd Law?

Mass is a measure of an object's inertia, or resistance to change in motion, while weight is a measure of the force of gravity acting on an object. In relation to Newton's 2nd Law, mass is a constant factor that affects an object's acceleration, while weight can vary depending on the strength of gravity. However, on Earth's surface, weight and mass are often used interchangeably since the strength of gravity is relatively constant.

Can Newton's 2nd Law be applied to objects in non-uniform motion?

Yes, Newton's 2nd Law can be applied to objects in non-uniform motion, as long as the net force acting on the object is known. In this case, the acceleration of the object will vary based on the changing force. This is often seen in objects moving in a circular path, where the acceleration is constantly changing due to the changing direction of the force acting on the object.

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