A block of mass 3.9 kg is sitting on a frictionless ramp with a spring at the bo

Question

A block of mass 3.9 kg is sitting on a frictionless ramp with a spring at the bottom, as shown, that has a spring constant of 555 N/m. The angle of ramp with respect to the horizontal is 23°.

Randomized Variables m = 3.9 kg k =555 N/m = 23°

A) The block, starting at rest, slides down the ramp a distance 79 cm before hitting the spring. How far, in centimeters does the spring compress before the block stops?

B) After the block comes to rest, the spring pushes the block back up the ramp. How fast, in meters per second is the block moving right after it comes off the spring?

C) What is the difference in Joules in the gravitational energy between the original position of the block at the top of the ramp and the position of the block when the spring is fully compressed?

Explanation / Answer

initial gravitational potential energy Ui = m*g*L*sin23

final elastic potential energy Uf = 0.5*k*x^2

Uf = Ui

0.5*555*x^2 = 3.9*9.8*0.79*sin23

x = 0.206 m = 20.6 cm

++++++++++++

B)

elastic potential energy = kinetic energy

3.9*9.8*0.79*sin23 = 0.5*3.9*v^2

v = 2.46 m/s <<<<<---------answer

__________________

C)

dU = m*g*(L+x)*sin23 = 3.9*9.8*(0.79+0.21)*sin23 =15 J

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