If a Mass of 125 kg is dropped from 6.6m straight down what will the velocity be when it lands?

Question

Been trying to work it out and research the net with no results. Could anybody give me a formula to get on the right track please.

Answer 1

Use the principle of conservation of energy to solve this question.

At the start, the energy of the mass is entirely potential = mgh.

When it hits the ground, all the potential energy has been converted to kinetic energy = 0.5*m*v^2

These must be equal

mgh = 0.5*m*v^2

v = SQRT(g*h/0.5)

v =SQRT(9.8*6.6/0.5)

v = 11.4 m/s

Answer 2

Solve this by thinking about how the potential energy is converted into kinetic energy.

At the start, the mass has potential energy but no kinetic.

E= mgh + 1/2 m v^2 = 125 x 9.8 x 6.6 + 1/2 x 125 x 0
E = 8085 J

At the end, the mass has no potential energy so it's all kinetic

E = mgh + 1/2 m v^2 = 125 x 9.8 x 0 + 1/2 x 125 x v^2

E = 62.5 v^2

But energy is conserved, so the initial energy is the same as the final energy

8085 = 62.5 v^2
v^2 = 129.36
v = 11.37

Answer 3

well, if u r talking about newtons laws of motion, you dont count with the mass, so, a nice equation would be :Vsquare= Usquare + 2gs

where V is the velocity that u r looking for, U is the iniatial velocity (that would be 0 because you drop it), g is the gravity (9.8 ms-2) and S is the distance, which is 6.6 m


however, if its in real life, the bigger the object, the more air resistance will have and is going to be quite hard to do it, because you will to calculate the viscous drag, and the upthrust, and the the weight

Answer 4

for this you need to use one of the suvat equations:

V^2 = U^2 + 2A*S

where V is velocity at the end U is start Velocity A is acceleration and S is displacement

the mass is irrelevant as all object accelerate at the same rate under gravity. i will assume we are on earth so g is 9.8 m/s^2

doing it this way you get a speed of 11.4 m/s

you could also do it by assuming that all of the objects potential energy is converted into kinetic therefore

P.E = mgh

K.E = (mv^2)/2

mgh = (mv^2)/2

the masses cancel so:

gh = v^2/2

v^2 = 2gh

this is exactly the same as for the suvat equation as the initial velocity is 0 and g is the acceleration under gravity so i wont bother putting the numbers in again

Answer 5

The formula is Vsquared = Usquared + 2xFxS where V is final velocity, U is initial velocity F is acc due to gravity in the units chosen and S is the distance fallen in same units. Since U is zero, V = square root (2xFxS). If you know the time of falling the formula is V=U+FxT

Answer 6

s = at^2
v=at
where s=distance, a=acceleration, v = velocity and t=time

s=6.6m, a = 10m/sec^2

Solve for t = (0.66)^(1/2) = 0.81

plug this value of t into the first order derivative (v = at)

0.81 sec * 10 m/sec^2 = 8.1 m/sec

and that's the velocity when the object has fallen 6.6 meters. The mass of the object is irrelevant.

Answer 7

first, velocity of a falling object is independent of the mass.

hence..
h=1/2 g t^2

this gives the time it takes to reach ground.

t=sqrt (2d/g)=1.1541 seconds..

substitute this into V=Vo -gt
the minus is because g is a vector pointing down.. so that..
Vo = 0, dropped from rest.

there fore we obtain, V= - 11.322 m/s

Answer 8

I've laid this out for you to follow easily..(I hope)

This is Kinetic Energy from Potential energy.
PE = mass(125kg) x g (9.81) x h (6.6)
125 x 9.81 x 6.6 = 8,093.25 Joules.
On landing, Loss in PE = Gain in KE
Therefore KE = 8,093.25 J

KE = ½mv² ....v = √(2 x KE)/m
v = √(2 x 8093.25)/125 = √16,186/125 = √129.5

Velocity = 11.4 m/s.

(That's my final answer).
...

Answer 9

Using the formula for uniformly accelerated motion, v^2 = u^2 + 2ax

u = 0m
a = 9.81ms^-2
x = 6.6m

therefore: v^2 = 2(9.81)(6.6)
v^2 = 129.4919...
v = 11.38ms^-1 (2d.p.)

Answer 10

Mass is irrelevant.
v^2 = 2*g*d (one of Kinematic equations)
v^2 = 2*9.8*6.6 = 129.36
v = sqrt(129.36) = 11.37 m/s

http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/1DKin/U1L6c.html

wrong direction I tried.
d = 0.5 * g * t^2
6.6 m = 0.5 * 9.8 m/s/s * t^2
t^2 = 6.6 / 4.9 s^2
t = sqrt(1.3469) s
t = 1.160