Answer: 30 degrees
Step-by-step explanation:
A pendulum consists of a small object hanging from the ceiling at the end of a string of negligible mass. The string has a length of 0.72 m. With the string hanging vertically, the object is given an initial velocity of 1.4 m/s parallel to the ground and swings upward in a circular arc. Eventually, the object comes to a momentary halt at a point where the string makes an angle θ with its initial vertical orientation and then swings back downward. Find the angle θ.
mv²/2= mgh=mgL(1-cosθ)
cosθ= 1- (v²/gL)
θ=arccos[1- (v²/gL)]
θ=arccos[1- (1.4²/9.8•0.75)] = 34.6°
A pendulum consists of a small object hanging from the ceiling at the end of a string of negligible mass. The string has a length of 0.80 m (0.75m). With the string hanging vertically, the object is given an initial velocity of 2.2 m/s (1.4m/s) parallel to the ground and swings upward in a circular arc. Eventually, the object comes to a momentary halt at a point where the string makes an angle θ with its initial vertical orientation and then swings back downward. Find the angle θ.
Using energy conservation,
1/2 mv^2 = mgL(1-cos(t))
Solve this equation for cos(t):
cos(t) = 1 - v^2/2gL
cos(t) = 1 - (1.4)^2/(2x9.8x0.75) = 0.8667
Now t = cos^(-1) (0.8667) = 30 degrees.