Determine acceleration given work done and vertical distance

In summary: If you assume that the work is done by the external lifting force and that there is no other work done on the mass, then the acceleration is indeed 11.5 m/s^2. However, if you consider the work done by gravity as well, then the acceleration is 21.5 m/s^2. In summary, the body with a mass of 10kg was raised vertically by a height of 2m with 230J of work done. Assuming the work was done by the external lifting force and neglecting gravity, the acceleration of the body is 11.5 m/s^2. However, if the work done by gravity is also taken into account, the acceleration is 21.5 m/s^2
  • #1
kaspis245
189
1
1. A body, whose mass is 10kg, is vertically raised upwards h=2 m . 230J work was done. Find the acceleration.

Homework Equations


W = Fh
F = ma

The Attempt at a Solution


W = Fh

F = A/h = 230J / 2m = 115J

F = ma

a = F/m = 115J/10kg = 11.5 m/s^2
 
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  • #2
The question is incomplete. The work done on what by what force?

If it is the work done by the lifting force on the mass, the acceleration of the mass is not only dependent on this force.
 
  • #3
So, what's the solution then?
 
  • #4
When a problem is (or even appears to be) incompletely specified, you should point that out, make some reasonable assumptions and state those assumptions along with your solution.

For instance you might assume that the work in question is that done by the external lifting force, excluding gravity.
 
  • #5
You need to solve it with the information given, which means you need to make some assumptions.

It could be useful to turn around the problem and think about what would have been the work done if there were no acceleration. With that clear, it could be easier to see how to solve the original situation.
 
  • #6
OK, I think now it's correct:

A = Fh

F = A/h = 230J/2m = 115N

F1 - mg = F

F1 = F + mg = 115N + 10kg*10m/s2 = 215 N

F1 = ma

a = F1/m = 215N / 10kg = 21.5 m/s2
 
  • #7
Well, except that the lifting force and gravity are working in different directions ...
 
  • #8
Hey, I have found another solution, but the answer is different:

A = Ek = mv2/2

V2 = 2A/m = 46 (m/s)2

V2 = vo2+2as

a = v2/ 2h = 11.5 m/s

So why is that?
 
  • #9
That solution has the same problem as your original one. It assumes that there is no gravitation.
 

What is the relationship between work done and acceleration?

The work done on an object is directly proportional to its acceleration. This means that as the work done on an object increases, its acceleration also increases. Similarly, if the work done decreases, the acceleration decreases as well.

How does vertical distance affect acceleration?

Vertical distance has a direct impact on acceleration. The greater the vertical distance an object travels, the greater its acceleration will be. This is because the object is gaining more potential energy as it moves higher, which is then converted into kinetic energy and results in a higher acceleration.

Can you determine acceleration given only work done and vertical distance?

Yes, it is possible to determine acceleration using only the values of work done and vertical distance. The formula for acceleration is acceleration = work done/vertical distance. However, it is important to note that this formula assumes that there are no other external forces acting on the object besides gravity.

How can I measure the work done and vertical distance of an object?

The work done on an object can be measured using the formula work done = force x distance. This requires measuring the force applied on the object and the distance it moves in the direction of the force. The vertical distance can be measured using a ruler, measuring tape, or any other measuring device.

Why is it important to determine acceleration given work done and vertical distance?

Knowing the relationship between work done, vertical distance, and acceleration is crucial in understanding the motion of objects. This information can be used to predict the behavior of objects and design experiments or devices that involve movement. Additionally, it helps in understanding the concept of energy and how it is converted from one form to another.

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