Question Video: Finding the Work Done by the Weight of a Body Sliding along an Inclined Plane

A body of mass 27 kg was placed at the top of a smooth inclined plane of height 4.5 m. It slid down the line of greatest slope until it reached the bottom of the plane. Calculate the work done by the weight of this body given that the acceleration due to gravity 𝑔 = 9.8 m/s².

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Video Transcript

A body of mass 27 kilograms was placed at the top of a smooth inclined plane of height 4.5 meters. It slid down the line of greatest slope until it reached the bottom of the plane. Calculate the work done by the weight of this body given that the acceleration due to gravity 𝑔 is equal to 9.8 meters per square second.

Remember, work is the measure of energy transfer when a force 𝐅 moves an object through a distance 𝑑. The force we’re interested in is the downwards force of the weight of the body. Let’s draw a picture of what’s going on. We’ve got a body of mass 27 kilograms. There is a downward force due to gravity. We call this weight. And we can calculate the value of this force by using the formula force is equal to mass times acceleration. The mass of the body is 27 kilograms and the acceleration due to gravity is 9.8 meters per square second, or let’s call that 𝑔. So, the weight is 27𝑔 in the downward direction.

We also know that the body is placed at a height of 4.5 meters. The fact that the plane is smooth means that there is no frictional force acting upon the body. And so, at this stage, we might be thinking we need to consider the length of the slope that the body moves down and the component of the weight that acts in this direction. In fact, the formula we used to calculate work done is the force multiplied by the distance traveled. Since the vertical height and the weight done are acting in the same direction, we can simply use the values we’ve got. That is work done is 27𝑔 multiplied by 4.5 or 27 times 9.8 times 4.5. That gives us 1190.7. But of course, work done is measured in joules.

The work done by the weight of the body, therefore, is 1190.7 joules.

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