- #1
SamLing2000
- 6
- 0
Homework Statement
A 1.18 kg block slides across a horizontal surface directly toward a massless spring with spring constant 5,803 N/m. The surface is frictionless except for a rough patch of length 0.42 m that has coefficient of kinetic friction 0.367. The initial velocity of the block is 2.49 m/s directed straight toward the spring. What is the maximum compression of the spring?
What i obtained form the question:
v0 = 2.49
friction coefficient 0.367
m=1.18
d=0.42
Spring constant = 5803
Homework Equations
W=Fd
W=Δk
k=1/2mv^2
The Attempt at a Solution
What I first did was find the knetic energy before the object hit the spring so i got
kf = .5(1.18)(vf)
ki = .5(1.18)(2.49)
i replaced vf with the equation to obtain equation is vf^2 = vi^2 + 2ax
kf = .5*(1.18)(2.49^2+2a(0.42))
Now i have W=Fd which i made W=(1.18)(a)(.42)
then i set the equations equal to each other
.5(1.18)(2.49^2+2a(.42))-.5(1.18)(2.49)=(1.18)(a)(.42)
solved for a = -1.029188469
used this a to find vf = 2.309887808
now i have the velocity it hits the spring with I then again brought back the work equation to find
W = kf-ki since final knetific force is 0 i have
W = -.5(1.18)vf^2 = Fd = ((-5803x)x)
then i solved for x as 0.0232911326
as demanded I entered 2.33 cm. But i was marked wrong. Can anyone help? That'll be greatly appreciated.