Physics Work: Velocity?
A point mass m = 174 g hangs from a string of length l = 1.73 m.
Calculate the value of v, so that the string reaches a maximum angle of θ = 44.4°.
A point mass m = 174 g hangs from a string of length l = 1.73 m.
Calculate the value of v, so that the string reaches a maximum angle of θ = 44.4°.
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Verified answer
The height raised by the mass is 1.73 – (1.73 . cos 44.4º) = 0.494 m
Height energy gained = KE lost
m . 9.81 . 0.494 = 0.5 . m . v^2
v^2 = 9.69
v = 3.11 m/s
See the website below for a picture of this type of problem.
http://www.stkate.edu/physics/phys111/BPSchematic....
The maximum velocity occurs when the object is at the lowest position. So, the maximum KE is at the lowest position. As the object swings upward, its kinetic energy decreases, and its potential energy increases.
KE at lowest position = PE at highest position
In the picture, L is the length of the string. When the string is vertical, the distance from the top of the picture to the object is L. As the object swings upward, the object moves upward the distance, âh.
PE at highest position = m * g * âh
âh = L – L * cos θ = 1.73 – 1.73 * cos 44.4Ë
PE at highest position = 0.174 * 9.8 * (1.73 – 1.73 * cos 44.4Ë)
KE at lowest position = ½ * m * v^2 = ½ * 0.174 * v^2
½ * 0.174 * v^2 = 0.174 * 9.8 * (1.73 – 1.73 * cos 44.4Ë)
Divide both sides by ½ * 0.174
v^2 = 2 * 9.8 * (1.73 – 1.73 * cos 44.4Ë)
v = [2 * 9.8 * (1.73 – 1.73 * cos 44.4Ë)]^0.5
v = 3.11 m/s