# Combining Newton's Laws and Kinematic

• gungo
In summary, Max (65 kg) pushes Toni (50 kg) with a force of 360 N. The force of friction is 0 on Toni and 80 on Max. Max's acceleration is 4.3 m/s^2 (left) and Toni's acceleration is 7.2 m/s^2 (right). If Max pushes Toni for 0.1 s, Toni will travel a distance of approximately 0.33 m. The slight discrepancy in the answer may be due to rounding errors or a difference in assumptions about the acceleration during the remaining 0.4 s.
gungo

## Homework Statement

Max (65 kg) pushes Toni (50 kg) with a force of 360 N. The force of friction is 0 on Toni and 80 on Max.
(a) Find each girls acceleration
(b) If Max pushes Toni for 0.1 s, how far will Toni travel in 0.5 s?

## Homework Equations

Fnet=ma
v2=v1+at
d=v1(t)+1/2a(t)^2

## The Attempt at a Solution

For (a), I got the correct answers by using Fnet=ma
Max's acceleration:4.3m/s^2 (left)
Toni's acceleration: 7.2m/s^2 (right)
For (b), Toni's acceleration is only 7.2 during the 0.1 seconds so...
d=v1(t)+1/2a(t)^2
d=(0)(0.1)+1/2(7.2)(0.1)^2
d=0.036
To find the distance for the remaining 0.4 seconds, I need to find v1 which is v2 of the 0.1 seconds
v2=v1+at
v2=7.2(0.1)
v2=0.72 m/s
So v1 for the 0.4 s is 0.72. I assumed acceleration is 0 during this time and that she is now moving at a constant velocity
d=0.72(0.4)+1/2(0)(0.4)^2
d=0.288
d1+d2=0.324
It's very close to the answer my teacher gave which is 0.33 m..but I'm just curious as to why it's a little off because it might be considered wrong on a test.

It's off probably because of round off errors. Carry the intermediate calculations to more decimal places and see what happens. Better yet, derive a symbolic answer and substitute the given quantities at the very end.

gungo

## 1. How do Newton's Laws and Kinematics relate to each other?

Newton's Laws and Kinematics are both fundamental concepts in physics that describe the motion of objects. Newton's Laws explain the causes of motion, while Kinematics deals with the mathematical description of motion. Together, they provide a comprehensive understanding of how objects move in the physical world.

## 2. Can Newton's Laws and Kinematics be used to solve real-world problems?

Yes, Newton's Laws and Kinematics are used extensively in the field of engineering and other sciences to solve real-world problems. They can be applied to a wide range of scenarios, from simple freefall motion to complex systems of interacting objects.

## 3. How do we combine Newton's Laws and Kinematics to analyze motion?

To analyze motion using Newton's Laws and Kinematics, we first identify the forces acting on the object and apply Newton's Second Law (F=ma) to determine the acceleration. Then, using the appropriate kinematic equations, we can calculate the object's displacement, velocity, and acceleration over time.

## 4. Are there any limitations to combining Newton's Laws and Kinematics?

While Newton's Laws and Kinematics are powerful tools for understanding motion, there are some limitations to their application. These include ignoring factors like air resistance, friction, and the non-uniform distribution of mass in an object. In certain scenarios, more advanced concepts such as calculus may be necessary for a more accurate analysis.

## 5. Can we apply Newton's Laws and Kinematics to non-inertial reference frames?

Yes, Newton's Laws and Kinematics can be applied to non-inertial reference frames, but additional factors such as centrifugal and Coriolis forces must be taken into account. In these cases, the equations and principles may be more complex, but the fundamental concepts still hold true.

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