A crate of mass 9.8 kg is pulled up a rough incline with an initial speed of 1.4
ID: 1603977 • Letter: A
Question
A crate of mass 9.8 kg is pulled up a rough incline with an initial speed of 1.44 m/s. The pulling force is 106 N parallel to the incline, which makes an angle of 19.2° with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 5.06m.
(a) How much work is done by the gravitational force on the crate?
(b) Determine the increase in internal energy of the crate-incline system owing to friction.
(c) How much work is done by the 106-N force on the crate?
(d) What is the change in kinetic energy of the crate?
(e) What is the speed of the crate after being pulled 5.06m?
Please circle/underline the answers. Thanks!
Explanation / Answer
work done = F*s*costheta
(a)
theta = 90
Wg = m*g*L*cos90 = 0
(b)
normal force n = m*g - F*sintheta
frictional force fk = uk*N
angle = 180
Wf = -uk*(m*g - F*sintheta)*L
Wf = -0.4*((9.8*9.8)-(106*sin19.2))*5.06 = -123.83J
---------------
(c)
theta = 19.2
WF = F*L*costhea
WF = 106*5.06*cos19.2 = 506.53 J
--------------
(d)
from work energy theorem
wtotal = change in KE
change in KE = WF + Wf = 382.7
(e)
change in KE = 382.7
(1/2)*9.8*(v2^2-1.44^2) = 382.7
v2 = 8.95 m/s <<<------answer
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.