How Do You Solve These Challenging Physics Problems?

[Placeboy]

Hi, I actually have a few questions that have been driving me insane. I been at this forever so any help is greatly appreciated!

1. A leaky faucet drips 56 times in 30.0s. What is the frequency of the dripping?

a. 0.54 Hz
b. 0.43 Hz
c. 1.9 Hz
d. 2.3 Hz

2. A rotating merry-go-round has an angular velocity of 0.184 rad/s Find the period of rotation of the merry-go-round.

a. 34.1 s
b. 13.6 s
c. 5.43 s
d. 3.91 s


3. What happens when a periodic driving force is applied to a vibrating system?

a. The system will stop vibrating and finally come to a stop.
b. The system will vibrate at the frequency of the driving force.
c. The system will vibrate at its natural frequency.
d. The system will exhibit chaotic motion.
e. It will vibrate at some multiple of the driving frequency (call a harmonic or "overtone").


4. If both the mass of a simple pendulum and its length are doubled, the period will

a. be unchanged.
b. increase by a factor of 1.4
c. increase by a factor of 4.
d. increase by a factor of 2.
e. increase by a factor of 0.71.


5. An object undergoing simple harmonic motion has an amplitude of 2.3m If the maximum velocity of the object is 10 m/s what is the object's angular frequency?

a. 4.4 rad/s
b. 4.8 rad/s
c. 4.0 rad/s
d. 3.5 rad/s

6. A mass on a spring has an angular oscillation frequency of 2.56 rad/s. The spring constant is 27.2 N/m and the system's kinetic energy is 2.92 J when t= 1.56s What is the oscillation amplitude? Assume that ∅= 0.00

a. 52.9 cm
b. 70.1 cm
c. 40.0 cm
d. 61.5 cm

 

[Matterwave]

Have you tried to do any of them?

 

[Loremaster]

A hint: frequency is the number of "things" that happen PER second, while period is the number of seconds it takes for some "thing" to happen.

It's a simplistic start, but a good way to conceptualize it if you've just been introduced to these quantities.

 

[Placeboy]

I have a set of 25 problems and I worked on them for about 6 hours straight. These were the only ones I couldn't figure out. I just don't know where to start so I signed up on this forum because I really need the help. Anything to start is great, thanks Loremaster!

 

[rwisz]

I understand the frustration of tackling tricky problems. However, it is important to approach them with a clear and logical mindset. For the first question, the frequency of the dripping can be calculated by dividing the number of drips (56) by the time (30.0s), resulting in an answer of 1.87 Hz. This does not match any of the given options, so it is possible that there may be a typo or error in the question.

Moving on to the second question, the period of rotation can be found by dividing 2π (representing one full revolution) by the angular velocity (0.184 rad/s), resulting in a period of approximately 34.1 seconds, which corresponds to option a.

For the third question, the answer is b. The system will vibrate at the frequency of the driving force. This is known as resonance, where an external force can cause a system to vibrate at its natural frequency.

For the fourth question, the correct answer is d. Doubling both the mass and length of a simple pendulum will result in an increase in period by a factor of 2. This can be derived from the equation T = 2π√(L/g), where T is the period, L is the length, and g is the acceleration due to gravity.

Moving on to the fifth question, the angular frequency can be found by dividing the maximum velocity (10 m/s) by the amplitude (2.3m), resulting in an answer of approximately 4.35 rad/s, which corresponds to option a.

Finally, for the last question, the oscillation amplitude can be calculated using the equation E = ½kA^2, where E is the kinetic energy, k is the spring constant, and A is the amplitude. Rearranging the equation, we get A = √(2E/k), which gives an amplitude of approximately 0.7 m or 70.1 cm, corresponding to option b.

I hope this helps in solving your tricky problems. Remember to always approach scientific problems with patience and a systematic approach. Good luck!