30 kg) rides a skateboard (m = 3.2 kg) at a speed of 4.2 m/s (a) How much girl (
ID: 1785264 • Letter: 3
Question
30 kg) rides a skateboard (m = 3.2 kg) at a speed of 4.2 m/s (a) How much girl (n the girl ba e todo to bring herself to a stop? (b) How far does she travel if it takes 60s 5 A young have work does to stop? (e) What is the magnitude of the stopping force? r You have two springs that have different spring constants. It takes 180 J of work to compress one of 0 the springs by 015 m. It takes 200 J of work to stretch the other spring by 0.25 m. Which spring is stiffer? (calculate each spring constant and compare) mid n aer 7. (EP) A box with a mass of 3.0 kg is accelerated from rest by a constant force across a floor at a rate of 1.7 m/s2 for 6.5s. How much work does the force do on the box? How much power is produced by the force in moving the box? 8. At a ski resort, a tow rope powered by an engine can tow a 60-kg skier (at a constant speed) up a 300-m hill that is inclinded at angle of 24° in 2.7 minutes. If the coefficient of kinetic friction between the skiers and the snow is 0.12, how much power does the engine produce if there are 30 such skiers on the rope at one time?Explanation / Answer
5)
work done = change in KE = (1/2)*m*(vf^2 - vi^2)
work = (1/2)*(30+3.2)*(0-4.2^2) = 292.824 J
(b)
distance = (vf+vi)t/2
diatance = (0+4.2)*6/2 = 12.6 m
(c)
F = m*a = m*(vf-vi)/t = (30+3.2)*(0-4.2)/6 = -23.24 N
magnitude = 23.24 N
================================
work done = (1/2)*k*x^2
for spring 1
W1 = (1/2)*k1*x1^2
180 = (1/2)*k1*0.15^2
K1 = 16000 N/m
for spring 2
W1 = (1/2)*k1*x1^2
200 = (1/2)*k2*0.25^2
K2 = 6400 N/m
spring1 is stiffer
==================
7)
speed after t = 6.5 s
v = vo + at = 0 + (1.7*6.5) = 11.05 m/s
work = change in KE
work = (1/2)*m*(v^2 - vo^2)
work = (1/2)*3*(11.05^2-0) = 183.15 J
power = work/time = 28.2 W
=========================
speed v = distance /time = (300*sin24)/(2.7*60) = 0.753 m/s
force exerted by rope F = mg*sintheta + fk
F = m*g*sintheta + uk*m*g*costheta
F = (60*9.8*sin24) + (0.12*60*9.8*cos24)
F = 303.6 N
power = F*v = 228.6 W <<<------ANSWER
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