# Complex Kinematics and Dynamics

• Vraj Patel
In summary, a person pushes a puck at a constant force of 20 Newton towards another puck 15 meters away. If the force is maintained, the puck will travel 2.65 meters before it strikes the other puck.
Vraj Patel

## 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)

#### Attachments

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Last edited:

Your images are on your private google drive, so the links are inaccessible to other members. Either type out your solutions as suggested, or at least use the UPLOAD facility to make the images local to the PF server.

Doc Al said:
I uploaded the photos from a local source, so you should be able to see my work. Thank you for taking the time to help me.

gneill said:
Your images are on your private google drive, so the links are inaccessible to other members. Either type out your solutions as suggested, or at least use the UPLOAD facility to make the images local to the PF server.
I uploaded the photos from a local source, so you should be able to see my work. Thank you for taking the time to help me.

Vraj Patel said:
I uploaded the photos from a local source, so you should be able to see my work. Thank you for taking the time to help me.

gneill said:
ok

gneill said:
I typed out all the steps I used.

## What is the difference between kinematics and dynamics?

Kinematics is the study of motion without considering the forces that cause the motion, while dynamics is the study of motion taking into account the forces that cause it.

## What is a complex kinematic system?

A complex kinematic system involves multiple moving parts that interact with each other, making the analysis of its motion more challenging compared to a simple system.

## How is velocity different from acceleration?

Velocity is the rate of change of an object's position over time, while acceleration is the rate of change of an object's velocity over time. In other words, acceleration measures how quickly an object's velocity is changing.

## What is the role of calculus in studying complex kinematics and dynamics?

Calculus is essential in studying complex kinematics and dynamics because it provides the tools needed to analyze continuous motion and changes in velocity and acceleration. It allows us to calculate instantaneous rates of change and make predictions about the behavior of a system.

## What real-world applications use complex kinematics and dynamics?

Complex kinematics and dynamics have numerous applications in various fields such as engineering, biomechanics, robotics, and aerospace. Examples include analyzing the motion of a car on a bumpy road, designing prosthetic limbs, and predicting the trajectory of a spacecraft.

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