In: Physics
The spring shown in the figure is compressed 52 cm and used to launch a 100 kg physics student. The track is frictionless until it starts up the incline. The student's coefficient of kinetic friction on the 30∘ incline is 0.19 .
Part A
What is the student's speed just after losing contact with the spring?
Express your answer to two significant figures and include the appropriate units.
Part B
How far up the incline does the student go?
Express your answer to two significant figures and include the appropriate units.
Given
k = 80000 N/m
m = 100 kg,
x = -0.52m
The student's coefficient of kinetic friction on the 30∘ incline is 0.19 .
by conservation of energy 1/2 kx^2 = 1/2 mv^2
v = sqrt(kx^2/m)
V = sqrt(80000*(-0.52)^2/100) m/s
v 14.71 m/s
b) here considering the energies involved as
0.5 kx^2+ mgh = mgh' +
F*s
hereF is frictional force = muek*mg cos theta,h' = d sdin theta
0.5 kx^2+ mgh = mgh' + F*s
0.5 k x^2 + mgh = mg d sin theta + mue k*mg cos
theta
substituting the values
0.5 *80000(-0.52)^2 + 100*9.8*10 = 100*9.8*d
sin 30 + 0.19*100*9.8 cos30
d = 41.744 m