A block is pushed against thespring with spring constantk (located on theleft-ha
ID: 1758116 • Letter: A
Question
A block is pushed against thespring with
spring constantk (located on theleft-hand
side of the track) and compresses the springa
distance 5.2 cm from its equilibriumposition
(as shown in the figurebelow).
The block starts at rest, isaccelerated by
the compressed spring, andslides across a
frictionless track except for asmall rough area
on a horizontal section of thetrack (as shown
in the figure below).
It leaves the trackhorizontally, flies through
the air, and subsequentlystrikes the ground.
What is the springconstant k ? Answer in
What is thespeed v of theblock when it leaves
the track? Answer inunits of m/s.
What is the totalspeed of the block when it
hits the ground?Answer in units of m/s.
Explanation / Answer
We can attack this with a bit of kinematics and energy conservationtogether. The way this works, we'll answer the questions inreverse. If we start with projectile kinematics ... Vertical impact fall speed = (2gh) = (2 * 9.8 * 2.1m) = 6.416 m/s Time to hit ground after fall = (2*h/g) = (2*2.1/9.8)= 0.6547 s Same as horizontal fall time, speed when it leaves the track = D / t = 3.83 m / 0.6547 s= 5.850 m/s Total speed hitting ground v =(V2vert +V2horiz)1/2 = (6.4162 + 5.8502)1/2 = 8.68 m/s Next, apply conservation of energy between when the block iscompressed, and just before it leaves the track. KEcompress + PEcompress =KEedge + PEedge + energylost to friction 1/2 k x2 = 1/2 mv2 + umgd k = 2/x2 * (1/2 m v2 + umgd) = 2/(0.052 m)2 * (0.5 * 0.450kg * 5.8502 +0.5*0.450*9.8*1.1) = 7.49 x 103 N/m
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