Use Conservation of Energy to solve problem 1A, and work done by non-conservativ

Question

Use Conservation of Energy to solve problem 1A, and work done by non-conservative forces for 1B at the top of a 31.0° inclined plane and encounters a spring. kV'm, rigidly attached to the plane. If the block's mass is 33.0 kg and it compresses the spring by 1.00m, find the distance the block travelled before it encountered the spring. 1.B. What length would the object have to slide along the ramp if now there is friction between the block and the incline, and the spring ends up being compressed by the same amount (1.00m)? The coefficient of kinetic friction is 0.2.

Explanation / Answer

Given,

theta = 31 deg ; k = 3400 N/m ; m = 33 kg ; x = 1 m

from conservation of energy

PE(spring) = PE(gravity)

1/2 k x^2 = m g h

h = k x^2/2 mg

h = 3400 x 1^2/2 x 33 x 9.81 = 5.25 m

using trigonometry

D = h/sin(theta)

D = 5.25/sin31 = 10.2 m

distance before spring:

d = D - 1 = 10.2 - 1 = 9.2 m

Hence, d = 9.2 m

b)If friction will be there

PE(gravity) = PE(spring) + Wf

m g h = 1/2 k x^2 + u m g cos(theta)

m g h = 0.5 x 3400 x 1^2 + 0.2 x 33 x 9.81 x cos31 = 1755.5 J

h = 1755.5/33 x 9.81 = 5.42 m

D = 5.42/sin31 = 10.52 m

d = 10.52 - 1 = 9.52 m

Hence, d = 9.52 m

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