A 1.5 kg block is connected by a rope across a 50 cm-diameter, 2.0 kg, frictionl
ID: 1692729 • Letter: A
Question
A 1.5 kg block is connected by a rope across a 50 cm-diameter, 2.0 kg, frictionless pulley, as shown in the figure. A constant 10 N tension is applied to the other end of the rope. Starting from rest, how long does it take to move 30 cm? Express answer in 2 sif figs..Explanation / Answer
the tension in the rope connected to the 1.5 kg block is T - mg = -ma where m is mass and a is linear acceleration (since a will accelerate down, mg >tension on the other side, we set a as a negative number) the pulley, assumed to be a disk, experiences a torque due to the difference in tension on either side of the pulley; this tension difference is (T-10), and the torque it generates is (T-10)R where R isthe radius of the pulley (0.25m) torques cause angular accelerations according to: torque = I alpha where I is the moment of inertia of the pulley and alpha is the angular acceleration the moment of inertia of a disk is 1/2 MR^2; M=pulley mass angular acceleration is related to linear acceleration via a=R alpha or alpha = a/R so we have torque = (T-10)R = 1/2 MR^2 (a/R) the R's cancel, leaving T-10 = 1/2 Ma since we also know that T-mg = -ma, we subtract these equations and get mg - 10 = ma +1/2Ma or a(m+M/2)=1.5kgx9.8m/s/s - 10N a=4.7/(1.5+1)=1.88m/s/s therefore, it takes a time given by dist=1/2 at^2 =>t=sqrt[2xdist/a] t=sqrt[2x0.3m/1.88m/s/s]=0.56s
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