One Dimensional Kinematics: Force

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.
  • #1
TG3
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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
 
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  • #2
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.
 
  • #3
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?
 
  • #4
Oh dear, the computer is right! I forgot about the weight. Sorry.
 

Related to One Dimensional Kinematics: Force

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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