Question Video: Finding the Mass of a Particle given Its Potential Energy on the Top of a Smooth Inclined Plane and Its Speed at the Bottom of the Plane | Nagwa Question Video: Finding the Mass of a Particle given Its Potential Energy on the Top of a Smooth Inclined Plane and Its Speed at the Bottom of the Plane | Nagwa

Question Video: Finding the Mass of a Particle given Its Potential Energy on the Top of a Smooth Inclined Plane and Its Speed at the Bottom of the Plane Mathematics • Third Year of Secondary School

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A body started sliding down the line of greatest slope of a smooth inclined plane. When it was at the top of the plane, its gravitational potential energy relative to the bottom of the plane was 1,830.51 joules. When it reached the bottom of the plane, its speed was 8.6 m/s. Find the mass of the body.

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Video Transcript

A body started sliding down the line of greatest slope of a smooth, inclined plane. When it was at the top of the plane, its gravitational potential energy relative to the bottom of the plane was 1830.51 joules. When it reached the bottom of the plane, its speed was 8.6 meters per second. Find the mass of the body.

When our object is at the top of the incline, it has a potential energy of 1830.51 joules. When it gets to the bottom of the inclined plane, itβs traveling at a speed of 8.6 meters per second. We can apply the principle of conservation of energy to determine our unknown mass. In equation form, the principle states that the total initial energy of a system is equal to the total final energy of the system.

Looking back at our diagram, we can see that our initial energy is all potential energy. And since the object is moving when it reaches the bottom of the inclined plane, the total final energy is kinetic energy. To find the mass, we need to expand out the kinetic energy. Recall that kinetic energy is equal to one-half ππ£ squared, where π is the mass of the object and π£ is the speed of the object. Substituting in the expanded form for the kinetic energy, we now have the potential energy at the top of the incline is equal to one-half ππ£ squared of the object at the bottom of the incline.

Plugging in the values given to us in the problem, we have a potential energy of 1830.51 and a speed of 8.6. To isolate the π, we multiply both sides by two. This cancels out the one-half on the right-hand side of the equation. Next, we divide both sides by 8.6 squared. This cancels out that term on the right side of the equation. This leaves us with only the term π on the right side of the equation. When we perform the calculations on the left side of the equation, we come up with 49.5. We are solving for the mass, which is measured in kilograms. The mass of the body that slid down the inclined plane is 49.5 kilograms.

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