Question

Use the worked example above to help you solve this problem. A solid, frictionless cylinder reel of mass M 2.60 kg and radius R = 0.397 m is used to draw water from a well (see Figure (a)). A bucket of mass m = 2.19 kg is attached to a cord that is wrapped around the cylinder. (Indicate the direction with the sign of your answer.) (a) Find the tension l' in the cord and acceleration a of the bucket. T = 8.00 N a = 6.15 ✓ m/s2 (b) If the bucket starts from rest at the top of the well and falls for 3.40 s before hitting the water, how far does it fall? -35.5 m EXERCISE HINTS: GETTING STARTED I'M STUCK! A hollow cylinder of mass 0.118 kg and radius 3.70 cm has a string wrapped several times around it, as shown in Figure (d). A string is attached to a rigid support and the cylinder allowed to drop from rest. (Indicate the direction with the sign of your answer.) (a) Find the acceleration of the cylinder. cylinder = 6.53 What direction is the acce eration, up or down? If up, then the answer should be positive. If down, then the answer should be negative. m/s2 (b) Find the speed of the cylinder when a meter of string has unwound off of it. ViCylinderi = 3.61 The spinning motion of the cylinder is irrelevant. If the center of the cylinder has a certain acceleration, and it is constant, you can use straight-line kinematics to relate the acceleration, distance fallen, and speed. m/s

Answer 1

a] Let the acceleration be a and tension in string be T.

By force equation, mg -T =ma

and by torque equation, TR = I*alpha

or T = I*alpha/R = mr^2*a/r^2 = ma

adding both equation , mg = 2ma

a = g/2 = - 4.9 m/s^2 answer

b] using third equation of motion,

v = sqrt(2as)

= sqrt(2*4.9*1)

= 3.13 m/s answer