Solving the Question of Units for Dropped Mass on Surface

[PAU-L]

I *think* this is right, but if there is something obviously wrong please tell me where


Ive got a mass of weight 'y' dropped onto a surface that can support 10y
there is no wind resistance
the mass starts from stationary and accelerates under gravity (assumed to be 9.8 m/s/s)
the distance is 3m

constant acceleration from stationary for s distance is v^2=2as. v^2=2(9.8)3=7.6 m/s
The kinetic energy of a particle of mass m moving at velocity v is 1/2*m*v^2 K=1/2(y)(7.6^2)=29.4y

so the particle would excede the resistance by 19.4y

with respects to the different units involved is this correct, or can i not take the resistance of the surface (measured in neutons) away from the kinetic energy of the particle (measured in joules) to get an answer because of the different units?

 

[Astronuc]

The kinetic energy of a particle of mass m moving at velocity v is 1/2*m*v^2 K=1/2(y)(7.6^2)=29.4y

The relationship between mass m and weight y is m = y/g.

Energy/work is equated to force * distance, so 1 Joule (J) = 1 Newton * 1 m = 1 N-m.


Force accelerates/decelerates a mass.

It would seem one needs to determine the deflection of the surface or the time needed to decelerate the mass y/g in order to determine the force.

http://hyperphysics.phy-astr.gsu.edu/hbase/impulse.html

 

[m2003]

I would first like to commend you for attempting to solve this question and providing a detailed explanation of your thought process. However, there are a few things that need to be addressed in order to accurately solve this problem.

Firstly, in order to accurately calculate the kinetic energy of the mass, we need to take into account its weight. The formula for kinetic energy is K=1/2*m*v^2, where m is the mass of the object. In this case, the mass is given as 'y', but we need to know its weight (in Newtons) in order to correctly calculate its kinetic energy.

Secondly, when calculating the kinetic energy of the mass, we need to use the same units for mass and velocity. In your calculation, you have used meters per second as the unit for velocity, but the mass is given in terms of 'y'. We need to convert 'y' to a unit of mass (such as kilograms) in order to use it in the formula.

Lastly, when considering the resistance of the surface, we need to take into account the force required to support the mass. This force is equal to the weight of the mass, which we have already calculated in the previous steps. Therefore, we cannot simply subtract the resistance (measured in Newtons) from the kinetic energy (measured in joules) to get an answer because they represent different quantities.

In conclusion, while your thought process and attempt to solve this problem is commendable, there are some errors in the calculation that need to be addressed in order to accurately solve the problem. It is important to use consistent units and take into account all relevant factors in order to arrive at a correct solution.