The sled shown in the figure leaves the starting point with a velocity of 20 m/s. Use the...

RESEARCH:

At an instant the sled has both potential energy and kinetic energy. Then the total energy at this instant is

. . . . . . (1)

When the sled starts from top of the first incline and reaches the second incline, it has lost energy due to friction given by

As the sled reaches the bottom of the second incline it has a kinetic energy

To reach the end of the second incline, it needs to have enough energy to cover the work due to friction as well as the gravitational potential energy at the top.

If, then it does reach the top and the speed can be determine as

. . . . . . (2)

If, then it does not reach the top and the heightthe sled reaches can be determine as

. . . . . . (3)

Here is the work done due to friction for section of the incline up to h.

SKETCH:

Figure shows the motion of the sled on the track contains incline planes and circle.

SIMPLIFY:

The initial total energy of the sled is given by

. . . . . . (4)

By applying Newton’s laws the work done by frictional force on incline plane is

From equation (2), the kinetic energy at the top is

. . . . . . (5)

Here,,,and, ,

CALCULATE:

According to the given information and the origin of the coordinate system we selected,

The initial total energy of the system is given from equation (4), we get

To calculate the kinetic energy at the top, we need to evaluate the values of,

Now, let us substitute the above values in equation (4), we get the kinetic energy at the top,