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, it’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 𝑚𝑣 squared, where 𝑚 is the mass of the object and 𝑣 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 𝑚𝑣 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 𝑚, 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
𝑚 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.
