If an object falls from $32.9184 m$ and a mass of $212.281 kg$ how hard does that object hit the ground? I somehow got $68,481.92N$ by using this formula I found: $$\frac 12 m v^2 = m g h$$
I'm not sure if I'm correct and would appreciate a second look from professionals. Thank you. I can provide more information if needed.
How we usually solve a question like this:
The question in your homework is asking you to calculate the force with which the object hits the ground (how hard). Although that's not a very good way of asking which quantity you're supposed to find, I'm assuming you are required to find force. Now, if you're just starting physics, you've probably studied Newton's Laws of motion. According to Newton's Second Law,
$$\sum F_{ext}=ma$$
or, the total external force is given by the mass of the body times the acceleration. While solving your given question, consider the acceleration the object has, and multiply it by its mass to get the force with which it'll hit the ground. Think about what the acceleration of the object will be in this case.
Also think about how the height from which the object is dropped will affect this value.
Explanation of the formula you used:
The formula you used is the conservation of mechanical energy. What it says is, that the object, when it's at some height $h$, has a gravitational potential energy. At this height, the object has the potential to do work.
When it reaches a height of zero, or ground level, it will have no more potential energy. Instead, this will be converted into a form of energy called kinetic energy, which all moving bodies possess. Since the gravitational field is a conservative force field, the path is irrelevant.
We can hence state:
All the potential energy becomes kinetic energy when the object falls due to gravity.
We hence write, $$\frac 12 mv^2=mgh$$
When you substitute the height and mass, this formula can give you: total energy of the object, or the velocity with which it hits the ground. However, neither of these are the quantities that you were looking for. So, in this case, it's better to use Newton's Second Law.
Note: If the question was asking you to find velocity, you should note that the velocity of an object dropped from a certain height is independent of the mass of the object. Verify this using kinematics as an exercise. Also, I recommend that you try to understand the concepts behind physics and how they work, rather than using calculators and converters. Those tools should be used once you have a strong grasp of the subject and you want the calculations bit sped up. Also, please keep units in mind. It's a good habit to write units along with your quantities, and add and multiply them along with your values. This will ensure you get the quantity you're looking for.
Well i am assuming the object doesn't bounce back after this.
You know that force=change in momentum ÷ time ,right? As object comes to rest after colliding, final momentum=0
So F=mv/t
So what you have done is found v using energy conservation. Mass m is already known.
But what else is missing?
You don't have the duration of collision!!
If you think about it, the time taken by the object to come to a halt is very low, so low that you basically see the object coming to rest almost instantaneously.
So if time is very low, then Force is gonna be very high(As time is in the denominator)
So unless you know the time, you cant calculate the force.
Extra info: Such forces that are very large and can produce a noticeable change in the momentum in a very short time interval are called IMPULSIVE FORCES
Hope it helped
