A box of mass m = 1.5 kg is compressed 0.50 m by a spring with a spring constant
ID: 1485631 • Letter: A
Question
A box of mass m = 1.5 kg is compressed 0.50 m by a spring with a spring constant of 425 N/m and held at rest. Upon release, the box slides across the floor and up a 2.0m high, 500 degree frictionless hill. Once it comes to the top of the hill, it exhibits projectile motion.
Assume the slope is frictionless and the floor is frictionless except a sticky spot 1.70 m long with a coefficient of kinetic friction of 0.46. Also, assume the object reaches its maximum speed v1 before it encounters this spot.
1. Find the speed v1 of the box once it reaches the top of the hill.
2. Find the total flight time of the box once it is launched from the hill.
Explanation / Answer
a)
let v is the speed of the block at the top of te hill.
Net workdone on block, Wnet = W_spring + W_friction + W_gravity
= 0.5*k*x^2 - mue_k*m*g*d - m*g*h
= 0.5*425*0.5^2 - 0.46*1.5*9.8*1.7 - 1.5*9.8*2
= 12.23 J
now use Work-energy throem.
Wnet = gain in kinetic energy
Wnet = 0.5*m*v^2
==> v = sqrt(2*Wnet/m)
= sqrt(2*12.23/1.5)
= 4.04 m/s <<<<<<<<<<<<<<----------------Answer
b) let t is the flight time.
Apply, -h = voy*t - 0.5*g*t^2
-h = -0.5*g*t^2 (since voy = 0)
t = sqrt(2*h/g)
= srt(2*2/9.8)
= 0.639 s <<<<<<<<<<<<<<----------------Answer
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