# Acceleration of a system due to gravity

• Sheepwall
In summary, you can use a variety of methods to make an object accelerate faster than gravity, provided that the mass of the object is greater than the mass of the object being accelerated.

#### Sheepwall

The problem was present in a physics 1 exam, and I'm reasonably sure I know the answer, yet my friend contradicts me in my conclusion.

## Homework Statement

Find magnitude of acceleration of system ABC. Masses of A, B and C are all equal and each has mass 2.00 kg. Let gravitational acceleration g = 9.81 m/s2. See figure below.

Disregard friction - castor, air, and surface.

## Homework Equations

Newtons 2nd law of motion:
F = m a (1)

## The Attempt at a Solution

The force on the whole system is gravity's effect on B and C (weight of B and platform C). Through (1):

F = (2)(2.00 kg)(9.81 m/s2) = 39.24 N

Acceleration on the whole system is then, under the above force: (Through (1) again):

a = (39.24 N)/[(3)(2.00 kg)] = 6.54 m/s2.

Obviously, the acceleration of A is directed horizontally, while B and C are accelerating downwards. Still, the acceleration of each objects will be the same, yet in their respective directions. It is this value which I am after.

Also, can someone less ignorant than I tell me if I am right in this:
Without other external forces (other than gravity), the system will never accelerate faster than 9.81 m/s2 and the less the mass of A (and the larger the mass of B and C, equivalently), the closer the systems acceleration will be to 9.81 m/s2.

Thank you in advance and I apologize for the triviality of the problem :s

Your analysis is complete and correct for the information you're wanting about the system. Any other questions?

Thanks for the (very) quick replies!

Bystander said:
Your analysis is complete and correct for the information you're wanting about the system. Any other questions?

If you don't mind, continuing on the theme of triviality; Could I make something accelerate faster than gravity using wheels and cables, like so (A):

Again, disregarding frictions. How should I think when finding acceleration and tensions in these kinds of "problems?"

If "A" is the larger mass, the unlabeled mass can be accelerated at greater than g; you've got the double (one and a halfle?) advantage with the pulley set-up. Think of an asymmetric see-saw, or catapult, with a large mass on the short end and a small mass on the long. Trebuchet. Might be a variety of other gravity driven "siege engines."

Okay, so comparing my previous image to the one below:

Here, gravity's pull on A (again, like you did, assuming that A's mass is greater than that of the unlabeled), displacing A the distance s, will do the same to the unlabeled weight. In the previous image, displacing A by s, would displace the weight by 2 times s (?). I assume it is harder to displace A in the previous image, then, seeing as the work done by gravity is double there?

Sheepwall said:
work done by gravity
Is the same. "mgh" is "mgh" regardless of how the pulley, ropes, are rigged. The length of rope you've got to move past a particular point to lift/lower "A" a distance "h" can be changed, and the force you have to apply to pull the rope can be many times greater or less depending on how much mechanical advantage you "rig" into the block(s) and tackle.

## 1. What is the acceleration of a system due to gravity?

The acceleration of a system due to gravity is the rate at which the system's velocity changes due to the gravitational force acting on it. It is commonly denoted by the symbol "g" and has a value of 9.8 m/s² on Earth.

## 2. How is the acceleration of a system due to gravity calculated?

The acceleration of a system due to gravity can be calculated using the formula a = F/m, where "a" is the acceleration, "F" is the force of gravity, and "m" is the mass of the system.

## 3. Does the acceleration of a system due to gravity vary on different planets?

Yes, the acceleration of a system due to gravity varies on different planets depending on their mass and radius. For example, the acceleration of a system due to gravity on the surface of Mars is about 3.7 m/s², while on the surface of Jupiter it is about 24.8 m/s².

## 4. How does air resistance affect the acceleration of a system due to gravity?

Air resistance can affect the acceleration of a system due to gravity by opposing the motion of the system and reducing its acceleration. This effect is more significant for objects with larger surface areas, such as parachutes, than for objects with smaller surface areas, such as bullets.

## 5. Can the acceleration of a system due to gravity be negative?

Yes, the acceleration of a system due to gravity can be negative if the force of gravity is acting in the opposite direction of the system's motion. This can occur when an object is thrown upwards, and gravity is pulling it back down. In this case, the acceleration due to gravity would be -9.8 m/s².