Question

1. A pendulum has a mass of 2.35 kg. If the pendulum swings back and forth 110 times in 90.0 seconds, what is the length of the pendulum?

2. A vertical spring is stretched 60.0 cm by a hanging 5.00 kg mass.

a. What is the spring constant?

b. What will be the frequency of vibration of this spring system? 

4. Determine the acceleration of a pendulum bob as it passes through an angle of 15 degrees to the right of the equilibrium point.

5. Radio telescopes receive waves from distant stars. If such a wave has a wavelength of 24 cm and travels at the speed of light (c = 3.00 x 108 m/s), what is the frequency?

6. The speed and wavelength of coastal water waves are 4.0 m/s and 6.0 m respectively. When the waves enter a shallower region, the speed decreases to 1.7 m/s. What is the wavelength in the shallower region?

Answer 1

1)

$$\frac{110}{90}=\frac{1}{2\pi}\sqrt{\frac{9.8}{l}}\\l=0.166\ m$$

2)

$$k=\frac{5(9.8)}{0.6}=81.7\frac{N}{m}$$

$$f=\frac{1}{2\pi}\sqrt{\frac{81.7}{5}}=0.643\ Hz$$

4)

$$a=9.8\sin{15}=2.5\frac{m}{s^2}$$

5)

$$f=\frac{3\cdot10^8}{0.24}=1.25\cdot10^9\ Hz$$

6)

$$f_1=f_2\\\frac{v_1}{\lambda_1}=\frac{v_2}{\lambda_2} \\\frac{4}{6}=\frac{1.7}{\lambda_2}\\\lambda_2=2.55\ m$$