Pre AP Physics Chapter 5:Work and Energy

 

Problems (130)

Solve the problems below on your own paper. Each problem must be solved on its own page. Be sure to use the 3-column method. Naturally, you are encouraged to use your formula/equation sheet. be sure that your boxed solutions are clearly marked with 'a', 'b', or 'c' etc.

 

                  1.   A 1.5 kN bag of toys is pulled 8 m up a 200 ramp into Santa’s Sleigh by 13 little elves. The little guys are able to exert a combined force of 1.8 kN parallel to the ramp. The coefficient of friction between the BOT and the ramp is 0.67.

a) Draw a FBD of the forces on the BOT.

b) Write the equation for the sum of all forces horizontal.

c) Write the equation for the sum of all forces vertical.

d) Calculate the net force on the BOT.

e) Calculate the change in the kinetic energy of the BOT.

 

                  2.   A mass of 0.5 kg is placed upon a weightless platform under which is a spring with at spring constant of 7.8 N/m. The spring is compressed 0.28 m. When the spring is once again fully extended the mass flies upwards!

a) Just how high will the mass go?

b) How much kinetic energy will the mass have?

c) How fast will the mass be going when it leaves the WP?

 

                  3.   Note the figure below: A ball of indeterminate mass is at point ‘A’. It slides to point ‘B’ along this frictionless track and at point ‘B’ the BOIM is moving horizontally. Next the ball proceeds to point ‘C’.

a) How long does it take the BOIM to go from point B to point C?

b) What is the horizontal velocity of the ball between points B and C?

c) What is the vertical displacement between points A and B?

d) What is the magnitude of h1?

e) You know the horizontal component of the ball at point C, what is the magnitude of the resultant velocity of the ball at point C?

 

Pre AP Physics Chapter 5:Work and Energy

Answer Section

 

PROBLEM

 

           1.     ANS:     

a) 

 

b)

c)

 

To find the net force we need to know the force of friction and the force parallel. The FBD tells us that the Force normal is equal to the force perpendicular. So we know these three things:

1) The force of friction:

2) The force parallel:

3) The applied force given to us in the problem.

We also know that the applied force is positive and the force of friction and the parallel force are negative.

 

So, the force net equation looks like this:

 

What do we do with this net force? To find the change in the kinetic energy we need this force because W or FNetd = DKE. This is simplicity itself:

The ‘d’ of course is the 8 m the elves pulled the BOT.

 

           2.     ANS:     

We know that work was done on the mass because its kinetic energy changed. We also know that the spring did work when it uncompressed. So we can write this equation to start things off:

We solve this equation for ‘d’ to get the height:

What is ‘F’? The only thing ‘F’ can be is weight. So this gives us

Well, what do you know! We now have both ‘F’ and ‘d’ so we must also know DKE! Use this familiar equation:

If we know the initial kinetic energy and if we know that the final kinetic energy is zero, at the top of the mass’s flight, we know that we can solve the KE equation for velocity:

 

           3.     ANS:     

a) First we will find the time it takes the ball to fall h2. Then we will find the horizontal velocity at that point.

The ball got this horizontal velocity by converting its GPE to KE while it fell the vertical distance between A and B. So, invoking the conservation of energy we write:

c)

d) Having found ‘h’ the sum of ‘h’ and h2 will give us h1.

e) The magnitude of the resultant velocity is simply the result of all of the GPE being converted into KE over the entire vertical displacement, or h1. We invoke the conservation of energy once again:

Remember that the ‘h’ is the entire vertical displacement.

 

I know what you are thinking! “But” you cry “The ball is going horizontally at point ‘B’. This means it stopped going vertically for just a bit of time. Therefore its final speed cannot simply be the square root of two gh.”

 

OK! Try this: You have two legs of a right triangle. You have the horizontal speed of the ball, form part ‘b’. Calculate the vertical speed of the ball using the same “square root of two gh” but this time for ‘h’ put in 1.6 m. You can do this because the initial vertical velocity is zero since the ball is going only horizontally at point B.

 

Having your two legs use your Pythagoras to find the final speed at C.

 

Word!