3. A 255 g ice cube slides down a ramp starting from...

3. A 255 g ice cube slides down a ramp starting from rest. The ramp has a 46° slope. After traveling 128 cm along the ramp, the cube strikes a spring of unknown spring constant. The coefficient of kinetic friction between the cube and the ramp is 0.17. If the maximum compression of the spring is 43 cm, what is its spring constant?

Transcript

0:00 Hello.

00:01 In this question, when the spring is compressed by a distance x, elastic potential energy pes get stored in the spring.

00:09 Since there is no friction, we can write pes is equal to p .e.

00:15 Ice, where p .e .i.

00:17 Denotes the potential energy of ice at the point where it starts reversing direction after releasing it.

00:24 So the elastic potential energy can be written as half k x squared equals p .e .i.

00:33 Can be written as m g h.

00:36 Here k is the spring constant and x is the distance of compression of the spring.

00:41 M is the mass of ice.

00:43 G is the acceleration due to gravity and h is the height of ice with respect to the bottom of the slope.

00:50 This equation can be rewritten for h as h is equal to k x square divided by 2mg.

01:00 Let's substitute the values.

01:02 So it equals k is 22 newton per meter into x is 10 centimeter in meters.

01:08 It can be written as 10 into 10 raised to minus 2 meter.

01:12 The whole square divided by 2 into mass of ice is 61 gram in kilogram.

01:19 It can be written as 61 into 10 raised to minus 3 kilogram into j is 9 .8 meter per second square.

01:29 So it equals 0 .184 meter.

01:34 Using trigonometric property in this diagram, the distance traveled by the ice through the slope can be written as delta s is equal to h divided by sine theta equals h is 0 .188.

01:50 Divided by sine 30 degree...

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