An object of mass 1 kg is made to slide down a smooth inclined plane of length 20m. If the kinetic energy possessed by the body at the bottom of the plane is 100 J, what is the inclination of the plane with the horizontal (in degrees)?
Take .
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
By the principle of conservation of energy, the final kinetic energy is equal to the initial potential energy. The gravitational potential energy is given by U = m g h , where m is the object's mass, g is the gravitational acceleration, and h is the height of the object above the ground. Thus, we have 1 0 0 = 1 ⋅ 1 0 ⋅ h , which gives h = 1 0 meters. Now let θ be the inclination of the plane. By the Law of Sines, 2 0 sin ( 9 0 ) = 1 0 sin θ . Therefore, θ = 3 0 degrees.