Mindblown: a blog about philosophy.
-
How Long is the String?
A 106 g ball is tied to a string. It is pulled to an angle of 7.80 degrees and released to swing as a pendulum. A student with a stopwatch finds that 17 oscillations take 13.0s. How long is the string? time period T = 2π √(L/g) 17 oscillations = 13 sec 1 oscillation (T) =…
-
Free-fall Acceleration
Astronauts on the first trip to Mars take along a pendulum that has a period on earth of 1.50 s. The period on Mars turns out to be 2.45 s. What is the Martian free-fall acceleration? Earth = 1.5 s Mars= 2.45 s T= 2π√L/g 1.5 s2 = (2π√L/9.8)2 1.5 s2 = 21.5 s2 = x L/9.81 1.5…
-
Frequency of Oscillation
In the aftermath of an intense earthquake, the earth as a whole “rings” with a period of 54 minutes. What is the frequency of this oscillation? T = 54 min / 1 x 60 s / m = 3.1 x 10-4
-
Degrees, Radians, and Sine Table
Compete the following table. 0 2 4 6 8 10 12 Complite second column. θ(rad) =0,3.490×10−2,6.980×10−2,0.1047,0.1396,0.1745,0.2094 sin(θ) =0,3.490×10−2,6.980×10−2,0.1045,0.1392,0.1736,0.2079
-
What is the Amplitude of Oscillation?
A passenger car traveling down a rough road bounces up and down at 1.5 Hz with a maximum vertical acceleration of 0.30 m/s2 both typical values. What is the amplitude of the oscillation? F= 1.5 Hz a= .30m/s2 amax = (2π f)2 x A 0.30m/s2 = (2π x 2.5)2 x A A = 0.30m/s2/(2π x 2.5)2 = .003377 m = .3377 cm…
-
What is the Spring Constant?
A spring is hanging from the ceiling. Attaching a 600 g mass to the spring causes it to stretch 18.0 cm in order to come to equilibrium. What is the spring constant? Known variables: m=600g g= 9.81 ΔL = 18cm k = mg/ΔL =(.6)(9.8 m/s2)/.18 = 3.27 N/m From equilibrium, the mass is pulled down 10 cm…
-
Determine the Maximum Speed
A 504 g mass oscillates with an amplitude of 13.0 cm on a spring whose spring constant is 25.0 N/m. Known variables: m = .504kg k= 25 N/m 1/2π √25N/m / .504kg) = .89 s Determine the maximum speed. F = 1/.89 =1.12 Vmax= 2π fA 2 x π x 1.12 x .13 =.9148 =.916 Determine the total energy. =1/2…
-
How Long is the Chain?
It is said that Galileo discovered a basic principle of the pendulum-that the period is independent of the amplitude-by using his pulse to time the period of swinging lamps in the cathedral as they swayed in the breeze. Suppose that one oscillation of a swinging lamp takes 5.5s How long is the lamp chain? 2π√(L/G)…
-
How Long Must You Hang On?
You and your friends find a rope that hangs down 19 m from a high tree branch right at the edge of a wide river. You find that you can run, grab the rope, and swing out over the river. You run at 2.0 m/s and grab the rope, launching yourself out over the river. How long must…
Got any book recommendations?