(796) Problern 13. A block of mass 5.9 kg is sitting on a frictionless ramp with
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(796) Problern 13. A block of mass 5.9 kg is sitting on a frictionless ramp with a spring at the bottom that has a spring constant of 595 N/m (refer to the figure). The angle of the ramp with respect to the horizontal is 39* Randomized Variables m=5.9kg k= 595 Nm A 33% Part (a) The block, starting from rest, slides down the ramp a distance 58 before hitting the spring. How far, in centimeters is the spring compressed as the block comes to momentary rest? sin0 cotan0 asin acos0 atan0acotansinh(0 cosh0tanhcotanh0 cosO tan END Degrees Radians Submit Hint I give up! Hints: 090 deduction per hint. Hints remaining: 2 Feedback: 0% deduction per feedback. 33% Part (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? 33% Part (c) what is the change of the gravitational potential energy, in Joules, 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
Given,
Mass, m = 5.9 kg
Spring constant, k = 595 N/m
Angle, theta = 39°
a) let us assume that x be the compresion
Apply law of conservation of energy
m x g x (d+x) x sin(39) = 0.5 x k x x2
5.9 x 9.8 x (0.58 +x) sin(39) = 0.5 x 595 x x2
36.39 x + 21.10 = 297.5 x2
by solving the above equation we get
x = 0.334 m or 33.4 cm
b) v = (2 x g x d x sin(39))1/2 = (2 x 9.8 x 0.58 x sin(39))1/2 = 2.67 m/s
c) delta U = m x g x (d+x) x sin(39) = 5.9 x 9.8 x (0.58 + 0.334) x sin(39) = 33.25 J
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