This discussion is closed.
droid
Badges: 0
#1
Report Thread starter 14 years ago
#1
A particle P of mass m is dropeed from a height h above the surface of the liquid in a container and falls freely under gravity intill it enters the liquid. As P enters the liquid, a quarter of its kinetic energy is lost. At time t after entering the liquid P has fallen a vertical distance of x through the liquid and the resistance to motion is 3mx^2. Calculate the speed of P when it has just entered the liquid and hence show taht its speed at time t later is given by:
v^2 = 2gx - 2x^3 + (3/2)gh

any help would be great thanks.
0
Gaz031
Badges: 15
Rep:
?
#2
Report 14 years ago
#2
(Original post by droid)
A particle P of mass m is dropeed from a height h above the surface of the liquid in a container and falls freely under gravity intill it enters the liquid. As P enters the liquid, a quarter of its kinetic energy is lost. At time t after entering the liquid P has fallen a vertical distance of x through the liquid and the resistance to motion is 3mx^2. Calculate the speed of P when it has just entered the liquid and hence show taht its speed at time t later is given by:
v^2 = 2gx - 2x^3 + (3/2)gh

any help would be great thanks.
First let us find its velocity immediately after entering the liquid:


Using the constant acceleration equations:
S=h, a=g, u=0, v=?=velocity before entering
v^2 = u^2 + 2as
v^2 = 2gh
KE before entering = 0.5m(2gh) = mgh
A quarter of KE is lost, hence is enters with (3/4)mgh of KE
KE = 0.5mV^2 = 0.75mgh
0.5V^2 = 0.75gh
V^2 = (3/2)gh

Considering motion inside the liquid:
f=ma
mg - 3mx^2 = ma
g-3x^2 = a
0.5v^2 = gx - x^3 + C
v^2 = 2gx - 2x^3 + k
x=0, v^2=(3/2)gh, k=(3/2)gh
Hence v^2 = 2gx - 2x^3 + (3/2)gh.
0
X
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of Surrey
    Postgraduate Open Afternoon Postgraduate
    Wed, 23 Oct '19
  • University of Bristol
    Undergraduate Open Afternoon Undergraduate
    Wed, 23 Oct '19
  • University of Exeter
    Undergraduate Open Day - Penryn Campus Undergraduate
    Wed, 23 Oct '19

Would you turn to a teacher if you were being bullied?

Yes (47)
25.41%
No (138)
74.59%

Watched Threads

View All