Please help! 1. A uniform-solid, cylinder of 5 cm radius is rolling along the fl
ID: 1582964 • Letter: P
Question
Please help!
1. A uniform-solid, cylinder of 5 cm radius is rolling along the floor with a constant speed of 80 cm/s.
a) What is the rotational speed of the cylinder about its axis? b) What is the magnitude and direction of the acceleration of a point on its surface?
c) At the instant a certain point on its surface is at the top of the cylinder, what is the velocity of the point?
d) Repeat if the point is at the contact with the floor.
e) Repeat if the point is midway between the top and floor and at the forward surface of the cylinder.
2. The cylinder rolls up an incline at an angle of 10 degrees. How long does it take to slow to a stop and how far does it roll up the incline?
Explanation / Answer
(a) w = v / r = 80 cm/s / 5cm
w = 16 rad/s
(B) a = w^2 r = 16^2 x 0.05 = 12.8 m/s^2
toward the central axis.
(C) v_top = v + w r = 160 cm/s
(D) v_bottom = v - wr = 0
(e) v_mid = v = 80 cm/s
2. KE = m v^2 / 2 + I w^2 / 2
= m v^2 /2 + (m r^2 / 2) (v/r)^2 / 2
= 3 mv^2 / 4
Applying energy conservation,
KEI + KEi = PEf + KEf
3 m v^2 / 4 + 0 = m g L sin10 + 0
3(0.80^2) / 4 = 9.8 L sin10
L = 0.282 m ....Ans
vf^2 - vi^2 = 2 a d
0^2 - 0.80^2 = 2(a)(0.282)
a =1.13 m/s^2
vf = vi + a t
0 = 0.80 - 1.13 t
t = 0.71 sec