# One Dimensional Kinematics: Force

• TG3
In summary, the conversation discusses finding the force exerted by a 0.3 kg ball when it hits the floor at a speed of 9.29 m/s. Two different approaches are mentioned, one using the equation vf^2 = v0^2 + 2A(x-x0), and the other using a v vs t graph. The final answer is found to be -2157 N, but it is later discovered that the computer is looking for the force due to gravity in addition to the force exerted by the floor.
TG3

## Homework Statement

A .3 kg ball is compressed a maximum of 0.6 cm when it strikes the floor at 9.29 m/s. Assuming acceleration is constant, what is the force the ball exerts on the floor?

## Homework Equations

vf^2 = v0^2 + 2A(x-x0)
Once I find A it will be easy, since
F=MA

## The Attempt at a Solution

0^2 = 9.29^2 + 2A (.006)
0 = 86.3041 + .012 A
-86.3041= .012A
-7192= A
F=MA
F=.3 (-7192)
F= -2157

That looks good to me! You have assumed constant acceleration, which probably isn't really right but which is probably a standard assumption in your course.

I actually did it a different way. I made a sketch of a v vs t graph, a straight line going from 9.29 at time 0 to zero at time t. The area under a v vs t graph is the distance .006. Using the area formula I was able to find the time t it takes for the ball to compress and stop. Then I used the idea that the slope on the v vs t graph is the acceleration. I got the same answer you have.

I found the "correct" answer: the computer wanted me to add the force due to gravity (.3 x 9.81) to the force exerted by the floor. This seems a bit conceptually shaky to me, but the computer said that was the correct answer. For my own future knowledge: is it, or was my first answer correct?

Oh dear, the computer is right! I forgot about the weight. Sorry.

## 1. What is one-dimensional kinematics?

One-dimensional kinematics is the study of motion in a straight line, where the only forces acting on an object are in the same direction as the motion.

## 2. What is force in one-dimensional kinematics?

Force in one-dimensional kinematics refers to a push or pull acting on an object, causing it to accelerate or decelerate in the direction of the force.

## 3. How is force related to one-dimensional motion?

In one-dimensional motion, force is directly proportional to the acceleration of an object. The greater the force, the greater the acceleration, and vice versa.

## 4. What are some examples of forces in one-dimensional kinematics?

Some examples of forces in one-dimensional kinematics include gravity, friction, tension, and applied forces such as pushing or pulling an object.

## 5. How does Newton's Second Law apply to one-dimensional kinematics?

Newton's Second Law, which states that force is equal to mass times acceleration, applies to one-dimensional kinematics by showing the relationship between force and acceleration in a single direction.

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