A circular saw blade with a radius of 0.145 m starts from rest and turns in a vertical plane with a constant angular acceleratio
n of 2.00 rev/s2. After the blade has turned through 155 revs, a small piece of the blade breaks loose from the top of the blade. After the piece breaks loose, it travels with a velocity that is initially horizontal and equal to the tangential velocity of the rim of the blade. The piece travels a vertical distance of 0.820 m to the floor.
How far does the piece travel horizontally, from where it broke off the blade until it strikes the floor?
How far does the piece travel horizontally, from where it broke off the blade until it strikes the floor?
1 answer:
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Answer:
41°
Explanation:
Kinetic energy at bottom = potential energy at top
½ mv² = mgh
½ v² = gh
h = v²/(2g)
h = (2.4 m/s)² / (2 × 9.8 m/s²)
h = 0.294 m
The pendulum rises to a height of above the bottom. To determine the angle, we need to use trigonometry (see attached diagram).
L − h = L cos θ
cos θ = (L − h) / L
cos θ = (1.2 − 0.294) / 1.2
θ = 41.0°
Rounded to two significant figures, the pendulum makes a maximum angle of 41° with the vertical.
