# Simple Work Problem Disagreeing with Kinematics

In summary, the conversation discusses a problem involving a box with a mass of 10 kg being accelerated by 10 m/s/s over a distance of 10 meters. Two methods are used to calculate the kinetic energy of the box, with one resulting in 1000 Joules and the other resulting in 500 Joules. The discrepancy is due to a missing factor of 1/2 in the calculation, and the dimensions used in the question suggest the use of a certain energy formula.
I have the following problem: "A box with a mass of 10 kg is accelerated by 10 m/s/s over a distance of 10 meters. What is the kinetic energy of the box (assuming no friction)"

Using work...

Work = K.E.
F * D = K.E.
m*a*D = K.E. = 10 kg * 10 m/s/s * 10 m = 1000 Joules

However, using kinematics...

x = vo*t + at^2
10 m = 0 m/s + 10 m/s/s * t^2
10 m/10 m/s/s = t^2
t = 1 sec (the time it takes the box to go 10 meters)

vf = vo*t + a*t
vf = a*t = 10 m/s/s * 1 s = 10 m/s

KE = 1/2*m*v^2 = 1/2*10kg*(10 m/s)^2 = 500 Joules

Where is this factor of 2 difference coming from? Is the issue coming from how the problem is written? Thank you for your help!

Welcome to PhysicsForums.
x = vo*t + at^2
Check this?

Thanks! This is what happens when I don't get enough sleep, I leave out a factor of 1/2!

The box takes sqrt(2) seconds to reach 10 meters, which gives a final velocity of 14.14 m/s. The kinetic energy is indeed 1000 Joules.

Sorry and thank you!

berkeman

berkeman
The dimensions used in the question are mass, acceleration and distance. Remind anybody of a certain energy formula that uses those and only those dimensions ?

## 1. What is a simple work problem?

A simple work problem is a type of physics problem that involves calculating the amount of work done on an object by a force. Work is defined as the force applied to an object multiplied by the distance the object moves in the direction of the force.

## 2. How is work related to kinematics?

Kinematics is the study of motion, including the position, velocity, and acceleration of objects. Work is related to kinematics because it involves calculating the force and distance involved in moving an object, which are key components of motion.

## 3. Can you give an example of a simple work problem?

Sure! Let's say you are pushing a box across the floor with a force of 50 newtons and the box moves a distance of 10 meters. To calculate the work done on the box, you would multiply the force (50 N) by the distance (10 m) to get a work of 500 joules.

## 4. What is the equation for calculating work?

The equation for calculating work is W = F * d, where W is work, F is force, and d is distance. This equation is derived from the definition of work as force multiplied by distance.

## 5. How does one disagree with kinematics in a simple work problem?

In a simple work problem, one might disagree with kinematics by questioning the accuracy of the measurements or assumptions used in the problem. For example, if the distance moved by an object is estimated rather than measured precisely, this could lead to disagreement with the calculated work value based on that distance.

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