Speed and coefficeint of friction

[imy786]

Homework Statement

Three smooth stones, A, B and C are initially at rest, in contact with each other on the smooth surface of a frozen lake. The masses of the stones are A = 400 g, B = 300 g and C = 120 g and the coefficient of sliding friction between the stones and the ice is μslide = 0.0150. An explosion between the stones causes them to fly apart across the surface of the ice. Stone A flies off due North with an initial speed of 4.50 m s−1. Stone B flies off due east with an initial speed of 6.60 m s−1.

Calculate the speed and direction of motion of stone C immediately after the
explosion. [10 marks]

Homework Equations

F=uR
momentum= mass*velocity
F=ma

The Attempt at a Solution

there isn't a collion taking place...so momentum formula i don't think needs to be used.

we need to calculate speed of C.

we know
mass of C= 0.12kg
μslide = 0.0150

F=ma = uR
0.12a= 0.015R

dont know R or a...?

need help here...

 

[e(ho0n3]

I think you need to know the amount of time the force of the explosion acted on the stones to solve this problem.

 

[Doc Al]

there isn't a collion taking place...so momentum formula i don't think needs to be used.

It's not a collision; it's an explosion. But in an explosion, just like in a collision, all the forces are internal so momentum is still conserved.

 

[imy786]

well any ideas how to do this?

 

[Dick]

Follow Doc's advice. Write down total momentum before and total momentum after and set them equal.

 

[imy786]

mometum before collision= momentum after collison
m1u1+ m2u2 + m3 u3 = m1v1 + m2v2+m3v3

m1= 0.4
m2= 0.3
m3=0.120
u1=4.5
u2=6.6

is this correct so far...?

 

[Dick]

Before the collision all of the velocities are zero. Your velocities had better be vectors as well - they are heading in different directions.

 

[imy786]

m1= 0.4
m2= 0.3
m3=0.120
u1=0
u2=0
u3=0
v1=4.5sin90
v2=6.6sin0
v3=?

0= 1.8sin 90+ 1.98sin0+ 0.12*v3

is this correct...and then eqauting to calculate v3.

 

[Dick]

A vector has two components, x and y. You need to keep track of both. If you call east the positive x-axis then the final velocities are (4.5,0) and (0,6.6).

 

[imy786]

taking momentum in x direction-
o= 0.3*6.6 + 0.12*v3
v3= -33meters/s in x direction

taking momentum in y direction
0= 0.4*4.5 + 0.12*v3
v3= -15 meters/sec in y direction

the speed of stone c is west= 33 meter/s
the speed of stone c is south=15meter/s

using phythagors theorm to calculate the total velocity of stonce c


1089+225=
1314

speed of c is aprox 36meters/sec in the south west direction

 

[Dick]

I think your numbers came out wrong on the x velocity - but otherwise ok.

 

[imy786]

in x direction speed should be -16.5 m/s not -33.

it this correct, and the rest of the method working out total speed is correct too?

 

[Dick]

If you are anxious about whether all of your answers are right, it's good to work out ways of checking them yourself. Eg. in this question the sum of the final momenta you get should equal the zero initial total momenta. A good quick check would just be to add them up. That would have caught the 33m/s problem. But yes, it's ok. Of course the pythagorean theorem is also ok.