Question

a greased piggy (563kg) starts out at the top of a frictionless slide with a speed of 3.2 m/s. the top of the slid is 4m abouve the barn floor and ends up delivering the piggy horizontally onto the friction free floor. after sliding for 3.2 m, it collides with a spring and compresses it by .24m.

draw a picture illustrating the problem, prividing important details.

what is the intital mechanical energy?

velocity at the bottom of slide, just prior to floor:_______

value of spring constant:______

amount of work done by non-conservative forces:_______

Answer 1

Here is the diagram from what the question states

4 m 3.2 m 0.24 m

-------------------------------------------------------------------

initial mechanical energy

E = mgh + 1/2mv²

E = 563 * 9.8 * 4 + 1/2 * 563 * 3.2²

E = 24952 J

-----------------------------------------------------------

velocity at the bottom of slide

use conservation of energy, at the bottom of slide, potential energy = 0

24952 = 1/2mv²

v = sqrt ( 2 * 24952 / 563)

v = 9.414 m/s

--------------------------------------------------------------------

the question mentions - piggy horizontally onto the friction free floor.

It means there is no friction on 3.2 m part

so,

we can just simply equate kinetic energy of piggy to the elastic potential energy of spring

1/2mv² = 1/2kx²

mv² = kx²

k = mv² / x²

k = 563 * 9.414² / 0.24²

k = 207935 N/m

--------------------------------------------------

I don't know why question is asking for amount of work done by non-conservative forces because there is no friction as per the question statement.