A.) A 9.1 kg block is released from rest on a frictionless inclined plane making
ID: 1332397 • Letter: A
Question
A.) A 9.1 kg block is released from rest on a frictionless inclined plane making an angle of 13.6° with the horizontal. Calculate the time it will take this block when released from rest to travel a distance of 0.1 m along the ramp.B.) A 5.6 kg block is on an incline with a coefficient of static friction of 0.68. If the angle that the ramp makes with the horizontal is increased gradually, at what angle between the incline and the horizontal will the block begin to slide down the ramp?
C.)A 7.7 kg block is on an incline with a coefficient of static friction of 0.50. The angle that the ramp makes with the horizontal is increased gradually, until the block begins to slide down the ramp. If you know that the coefficient of kinetic friction between the block and the plane is 0.26, find the time it will take the block to slide down the ramp a distance of 0.83 m starting from rest. A.) A 9.1 kg block is released from rest on a frictionless inclined plane making an angle of 13.6° with the horizontal. Calculate the time it will take this block when released from rest to travel a distance of 0.1 m along the ramp.
B.) A 5.6 kg block is on an incline with a coefficient of static friction of 0.68. If the angle that the ramp makes with the horizontal is increased gradually, at what angle between the incline and the horizontal will the block begin to slide down the ramp?
C.)A 7.7 kg block is on an incline with a coefficient of static friction of 0.50. The angle that the ramp makes with the horizontal is increased gradually, until the block begins to slide down the ramp. If you know that the coefficient of kinetic friction between the block and the plane is 0.26, find the time it will take the block to slide down the ramp a distance of 0.83 m starting from rest. B.) A 5.6 kg block is on an incline with a coefficient of static friction of 0.68. If the angle that the ramp makes with the horizontal is increased gradually, at what angle between the incline and the horizontal will the block begin to slide down the ramp? C.)A 7.7 kg block is on an incline with a coefficient of static friction of 0.50. The angle that the ramp makes with the horizontal is increased gradually, until the block begins to slide down the ramp. If you know that the coefficient of kinetic friction between the block and the plane is 0.26, find the time it will take the block to slide down the ramp a distance of 0.83 m starting from rest.
Explanation / Answer
A)
gravitational force component down the plane = m*g*sin13.6
net force = m*a
m*g*sin13.6 = m*a
a = g*sin13.6
s = 0.1 m
from equations of motion
s = vo*t + 0.5*a*t^2
0.1 = 0 + 0.5*9.8*sin13.6*t^2
t = 0.29 s
++++++++++++++
B)
on the incline
normal force N = m*g*costheta
gravitaitonal force Fg = m*g*sintheta
frictioan force fs = us*N
the body begins to slide the Fg = fs
m*g*sintheta = us*m*g*costheta
tantheta = us = 0.68
theta = tan^-1(0.68)
theta = 34.22
(C)
angle = tan^-1(0.5) = 26.6
when the block slides
Fnet = Fg - fk = F - uk*N
Fnet = m*g*sin26.6 - uk*m*g*cos26.6
Fnet = m*a
a = g*(sin26.6 - uk*cos26.6)
a = 9.8*(sin26.6-(0.26*cos26.6))
a = 2.11 m/s^2
given s = 0.83 m
s = vo*t + 0.5*a*t^2
0.83 = 0 + 0.2*2.11*t^2
t = 1.4 s
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