Question Video: Finding the Distance a Body Moved under the Work Done by an Unknown Force given the Change in Acceleration

A force acted on a body of mass 400 g which had been at rest causing it to accelerate at 36 cm/s². If the work done by this force was 0.72 joules, find the distance the body moved.

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Video Transcript

A force acted on a body of mass 400 grams, which had been at rest, causing it to accelerate at 36 centimeters per square second. If the work done by this force was 0.72 joules, find the distance the body moved.

Remember, work is the measure of energy transfer when a force 𝐹 moves an object through a distance 𝑑. The formula we use to calculate work done is force times distance traveled. Now, it’s worth noting that we need to be really careful when dealing with units in these sorts of questions. If work done is measured in joules, this is because the force is measured in newtons and the distance is measured in meters. Now, let’s look individually at the force.

The formula for force is mass times acceleration. And, in turn, for the force to be measured in newtons, the mass needs to be measured in kilograms and the acceleration needs to be measured in meters per square second. We know that the work done is measured in joules, but the mass is measured in grams, and the acceleration is measured in centimeters per square second. And so, in order to link the work done in joules with the force, we need to begin by calculating the force in newton.

And so, let’s convert the measurement for mass into kilograms by dividing by 1000. 400 divided by 1000 is 0.4. So, the body has a mass of 0.4 kilograms. Similarly, we can divide the measure for acceleration by 100 to convert from centimeters per square second into meters per square second. That gives us that the acceleration is 0.36 meters per square second. We can now say that the force measured in newtons must be 0.4 times 0.36, giving us a force of 0.144 newtons.

We’ll now substitute this value and our value for the work done into the work done formula. We see that 0.72 must be equal to 0.144 times 𝑑, the distance traveled. And so, we solve for 𝑑 by dividing through by 0.144, giving us a value of five. Remember, we converted our acceleration into meters per square second. So, we can say that our distance must be measured in meters. The distance the body moved is five meters.

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