**93. ssm A penguin slides at a constant velocity of 1.4 m/s down an icy incline. The incline slopes above the horizontal at an angle of 6.9°. At the bottom of the incline, the penguin slides onto a horizontal patch of ice. The coefficient of kinetic friction between the penguin and the ice is the same for the incline as for the horizontal patch. How much time is required for the penguin to slide to a halt after entering the horizontal patch of ice?

We need to break this into two parts.  Part 1 we have the penguin sliding down the incline with a constant speed of 1.4 m/s.  At the bottom of the incline we have the same speed and now we want to know how long will it take to stop it on the flat ice.  So we know our final speed is zero.  We know our acceleration from sum of the forces and we can use kinematics to find the time.

The kinematic equation we need is

 

Solving for t

We get a from Newton’s second law

Solving for a

We can get fk from summing equations on the incline.

 

Since there is no motion in the perpendicular direction of the bicyclist on the hill, there is no acceleration perpendicular.

 

Since the penguin is traveling at constant speed down the incline, there is no acceleration down the incline.

 

But we know

Solving for

So now we have , on the flat part we can find the new friction force

Now sum forces on the flat part

Since penguin is not moving vertically on flat ice, acceleration vertically is zero.

 

 

So

 

 

 

 

 

 

Please send any comments or questions about this page to ddonovan@nmu.edu

This page last updated on January 11, 2020