Please read each question carefully. Show all work and the equations used. Clear
ID: 1322316 • Letter: P
Question
Please read each question carefully. Show all work and the equations used. Clearly identify the answer and the units. Use 3 significant digits in all your answers. Solve the problem completely. A solid block of mass 65.0 kg starts from rest and slides down a rough surface with a length of 10.0 m where the coefficient of friction is muk = 0.30. The surface is inclined at 50.0degree. After sliding 10.0 meters down the incline it slides onto a flat surface with kinetic coefficient of friction of 0.15 moves 5.00 m. It then hits a spring with a spring constant of ks = 500.0 N/m. Draw a freebody Diagram indicating all forces. Write out and solve the force and energy equations.Explanation / Answer
A)
h = L*sin(50)
= 10*sin(50)
= 7.66 m
-----------------
N = m*g*cos(50)
= 65*9.8*cos(50)
= 405.46 N
------------------
fk = N*mue_k
= 405.46*0.3
= 121.64 N
------------------
Fnetx = m*g*sin(50) - fk
= 65*9.8*sin(50) - 121.64
= 366.33 N
---------------------
a = Fnetx/m
= 366.33/65
= 5.63 m/s^2
==================================================
B)
delta U = -m*g*h
= -65*9.8*7.66
= -4879.42 J
----------------
change ineral enrgy = fk*L
= 121.64*10
= 1216.4 J
---------------------------
Wnet = chnage in KE
W_gravity + W_friction = KE
m*g*h - mue*fk = KE
KE = 4879.42 - 1216.4
= 3663 J
------------------
KE = 0.5*m*v^2
==> v = sqrt(2*KE/m)
= sqrt(2*3663/65)
= 10.62 m/s
------------------------
t = (v-u)/a
= (10.62-0)/5.63
= 1.885 s
----------------------
Wnet = Fnet*v
= 366.33*10.62
= 3890.4 Watts
=====================================================
C)
change in inenral enrgy = workdone by friction
= mue_k*m*g*d
= 0.15*65*9.8*5
= 477.75 J
-----------------
KEf = KEi - workdone by friction
= 3663 - 477.75
= 3185.25 J
-----------------------
KEf = 0.5*k*x^2
x = sqrt(2*KEf/k)
= sqrt(2*3185.25/500)
= 3.57 m
-----------------------
PE = KEf
= 3128.25 J
-----------------
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