Answer:
(a)10.5 rad/s2
(b) 20.9 rev
(c) 47.27 m
Explanation:
As the block of mass 53 kg is falling and pulling on the rope. The tension force on the rope must be equal to the gravity acting on the block according to Newton's 3rd law
T = mg = 53*9.81 = 519.93 N
Since this tension force would rotate the cylinder freely without any friction. The torque created by this tension force is
To = TR = 519.93 * 0.36 = 187.17 Nm
This solid cylinder would have a moment of inertia around it's rotating axis of:
(a)We can use Newton's 2nd law to calculate the angular acceleration exerted by such torque on the solid cylinder
(b) With such constant angular acceleration, the angle it would make after 5s is
Since each revolution equals to of angle, we can calculate the number of revolution it makes
(c) Assume the thickness of the rope is negligible (and its wounded radius is unchanging), we can calculate the rope length unwinded after rotating 131.3rad
Answer: 0.9264 kg
Explanation: [I'll use "cc" for cubic centimeter, instead of cm^3.
The volume is 6cm*4cm*2cm = 48 cm^3 (cc).
Density of Au is 19.3 g/cc
Mass of gold = (48 cc)*(9.3 g/cc) = 926.4 grams Au
1 kg = 1,000 g
(926.4 grams Au)*(1 kg/1,000 g) = 0.9264 kg, 0.93 kg to 2 sig figs
At gold's current price of $57,500/kg, this bar is worth $53,268. Keep it hidden from your lab partner (and instructor).
Answer:
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