A 2.0 kg rock is pressed up a distance delta x 20 cm against a spring with sprin

Question

A 2.0 kg rock is pressed up a distance delta x 20 cm against a spring with spring constant 400 N/m and then released causing it to slide across a friction less bore mill surface and then to slide down a frictionless incline At the bot loin of the incline is a horizontal surface that has a coefficient of kinetic friction mu_i = 0.80 with the rock, which causes tin- rock to come to test in L 1.5 m. Fill out the Energy Chart below to calculate the Potential and Kinetic Energy at each time point. Use g 10 m s^2 for easier calcination Assume Energy Conserved UNTIL the rock reach the rough surface.

Explanation / Answer

assume that initial height is h.

then initial gravitational potential energy =m*g*h=2*10*h=20*h Joules

initial spring potential energy=0.5*spring constant*compression^2=0.5*400*0.2^2=8 J

initial kinetic eenrgy =0 (as the rock is stationary)

hence initial total energy=20*h+8 joules

when the rock comes to the bottom of the incline, total potential energy=0

let speed be v m/s

then total kinetic energy=0.5*2*v^2=v^2 joules

as energy is conserved,

v^2=20*h+8....(1)

deceleration due to friction=friction coefficient*g=0.8*10=8 m/s^2

while travelling from B to C:

initial speed=v m/s

acceleration=-8 m/s^2

distance covered=1.5 m

final speed=0

using the formula:

final speed^2-initial speed^2=2*acceleration*distance

==>0^2-v^2=2*(-8)*1.5

==>v^2=24...(2)

using equation 2 in equation 1,

20*h+8=24

==>20*h=16

==>h=16/20=0.8 m

hence the table can be filled as below:

PE_gravity :

in scene A, h=0.8 m

==>PE_gravity=2*10*0.8=16 J

in scene B and scene C , height=0

==>PE_gravity=0

KInetic energy:

in scene A: speed=0==>kinetic energy=0

in scene B: kinetic energy=0.5*m*v^2=0.5*2*24=24 J

in scene C: speed=0==>KE=0

PE_spring:

in scene A, spring energy=8 J

in scene B and scene C, as compression =0, spring energy =0

table is filled as below:

  

scene A Scene B Scene C PE_gravity 16 J 0 J 0 J KE 0 J 24 J 0 J PE_spring 8 J 0 J 0 J

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