Question

Section H Name: Date Attend: review Problem: State the question and the situation in 2 sentences. You are to design a "Vibro-Skier Joy Ride"" that has the following characteristics. A 100 kg skier wearing a Velcro vest coasts down a 100 m long 37 slope that has a coefficient of friction between it and the skis of 0.20. At the bottom, the skier enters a level, frictionless surface on which a spring is located. The end of the spring has rollers and a Velcro cushion. The skier should compress the spring 3.0 m before stopping. The skier attached to the Velcro will get a nice vibrational ride at the end of the spring and the clastic and kinetic energy is converted to thermal energy due to the small friction between the skis and the snow on the level surface. What fun. In building the device, you are to determine the spring constant of the spring needed for the device. Plan: We often have to solve a problem and don't know the best plan. One way to find out is to start them all It there energy information? If so, draw an Energy-Bar diagram & write the Work- Energy equation. Is there force information in the problem? If so, draw a FBD & list force equations. Is there motion in the problem? If so, draw a MD & List Motion equations. Solve the Problem: Answer the question: Be sure to include units. Evaluate: Do a unit analysis (if you didn't do one above). How is the magnitude of the answer reasonable? Attend10

Answer 1

Normal friction mgsin@ Mgcos@ 37 Weight

From FBD

macos@

=Amgcos

acceleration is given by

- umgcos@ ma =mgsin@

- ucos@) a = g (sin@

from the values given in question we find

a =4.4ms

So, now we find the velocity of the rider at the end of the slope.

He starts from rest and acceleration is constant as we derived from the equation above

So, linear equation of motion is valid

$v^{2}-u^{2}=2as$

u= 0 as he starts from rest and a is acceleration and s is the distance.

2* 4.4 * 100 v

v=29.7ms

now as the rider hits the spring it starts to decelerate as the spring opposes the motion of the rider.

Suppose the maximum contraction of the spring is x m

So, from energy equation we get

Work done by the spring = change in kinetic energy

= -mu 2 2

2 i = mu

x=3m given in question

100 29.62 32

k=9777.78N/m, which is the required solution

any doubt feel free to comment