The box has a mass m and slides down the smooth chute having the shape of a parabola. If it has an initial velocity of v0 at the origin determine its velocity as a function of x. Also, what is the normal force on the box, and the tangential acceleration as a function of x?

,,

Explanation:

An expression for the velocity can be derived by applying the Principle of Energy Conservation:

Let assume that chute is frictionless, so that box is moved because of gravity. The equations of equilibrium for the box are:

The expression for the radius of curvature and trigonometric functions are, respectively:

Let assume that chute has the following form:

First and second derivatives of the function are, respectively:

Trigonometric functions and radius of curvature are:

The velocity as a function of x is:

The normal force on the box as a function of x is:

The tangential acceleration on the box as a function of x is:

when heated, the valance electrons increased their speed and transferred the heat from electron to electron.   i just took the test.

  distance on the y-axis and time on the x-axis.

explanation:

the instantaneous velocity = change in position/time taken

the slope of the graph should give instantaneous velocity.

  slope of a graph = change in value of y -axis / change in values of x -axis

  comparing both the equations

    change in value of y -axis = change in position

  change in values of x -axis = time taken

so position values should be on the y axis and time values should be on the x axis.

distance on the y-axis and time on the x-axis.