# Complex Kinematics and Dynamics

## Homework Statement

Two pucks (5 kg each) made of Teflon are on a long table, also made of Teflon. Puck A is sitting at
rest on the left end of the table. Puck B is 15 m away at the right hand end of the table, and is
travelling toward Puck A with an initial speed of 0.5 m/s. A person on the left waits 1.5 seconds and
then pushes Puck A forward from rest with a force of 20 N applied at an angle of 30° to the horizontal.
If that force is maintained at a steady rate for the entire question, how far will puck A travel before it
strikes puck B? (The coefficient of friction between the Teflon and Teflon is 0.04.

2. The attempt at a solution:

Puck A
Fax = 20NSin30
Fax = 10N

Fay = 20NCos30
Fay = 17.32N

Fg = mg
Fg = (5kg)(9.8m/s^2)
Fg = 49N

Fn = Fay + Fg
Fn =17.32N + 49N
Fn = 66.32

Ff = uFn
Ff = (0.04)(66.32N)
Ff = 2.65

Fnet = Fax - Ff
Fnet = 10N - 2.65
Fnet = 7.35N

a = Fnet/m
a = 7.35N/5kg
a = 1.47m/s^2

d = v1t + 1/2at^2
15-x = 1/2(1.47)(y-1.5)^24
x = -0.74y^2 + 2.22y +13.33

Puck B
Fg = mg
Fg = (5kg)(9.8m/s^2)
Fg = 49N

Ff = uFn
Ff = (0.04)(49N)
Ff = 1.96N

Since there is no applied force Fnet = -Ff

a = Fnet/m
a = -1.96/5kg
a = -0.39m/s^2

d = v1t + 1/2at^2
x = (0.5)(y) + 1/2(-0.39)(y)^2
-0.74y^2 + 2.22y +13.33 = 0.5 - 0.195y^2
0 = 0.545y^2 - 1.72y-13.33

I then put it in the quadratic formula and got:
y = 6.77s and y = -3.61s(omited)

Puck A Distance
d = v1t + 1/2at^2
d = (0m/s)(6.77s-1.5s) + 1/2(1.47m/s^2)(6.77-1.5s)^2
d = 20.41m(This answer doesn't make sense)

BvU
Homework Helper
Hi,

First thing that comes to mind is your decomposition of the 20 N in ##F_x## and ##F_y## ...

Second thing I notice is that you deleted part 2 of the template -- not good !
Third is I miss a list of variable names. What is ##d## ? (and: are you sure that is what you think it is ? -- a drawing might help an awful lot here ! )

hmmm27
haruspex
Homework Helper
Gold Member
an angle of 30° to the horizontal.
Pushing down or pushing up?

BvU
Homework Helper
Let's assume pushing down

Pushing down or pushing up?
pushing down

Hi,

First thing that comes to mind is your decomposition of the 20 N in ##F_x## and ##F_y## ...

Second thing I notice is that you deleted part 2 of the template -- not good !
Third is I miss a list of variable names. What is ##d## ? (and: are you sure that is what you think it is ? -- a drawing might help an awful lot here ! )
d represents distance.

Hi,

First thing that comes to mind is your decomposition of the 20 N in ##F_x## and ##F_y## ...

Second thing I notice is that you deleted part 2 of the template -- not good !
Third is I miss a list of variable names. What is ##d## ? (and: are you sure that is what you think it is ? -- a drawing might help an awful lot here ! )
I tried to upload a photo of my diagram but it wouldn't let me, but the pucks are heading toward each other.

BvU