D. The red car is moving faster than the blue car
Answer:
3331.5 kg
Explanation:
Given:
Spring constant of the spring (k) = 24200 N/m
Frequency of oscillation (f) = 0.429 Hz
Let the mass be 'm' kg.
Now, we know that, a spring-mass system undergoes Simple Harmonic Motion (SHM). The frequency of oscillation of SHM is given as:
![f=\frac{1}{2\pi}\sqrt{\frac{k}{m}}](https://tex.z-dn.net/?f=f%3D%5Cfrac%7B1%7D%7B2%5Cpi%7D%5Csqrt%7B%5Cfrac%7Bk%7D%7Bm%7D%7D)
Rewrite the above equation in terms of 'm'. This gives,
![2\pi f=\sqrt{\frac{k}{m}}\\\\Squaring\ both\ sides,\ we\ get:\\\\(2\pi f)^2=\frac{k}{m}\\\\m=\frac{k}{4\pi^2 f^2}](https://tex.z-dn.net/?f=2%5Cpi%20f%3D%5Csqrt%7B%5Cfrac%7Bk%7D%7Bm%7D%7D%5C%5C%5C%5CSquaring%5C%20both%5C%20sides%2C%5C%20we%5C%20get%3A%5C%5C%5C%5C%282%5Cpi%20f%29%5E2%3D%5Cfrac%7Bk%7D%7Bm%7D%5C%5C%5C%5Cm%3D%5Cfrac%7Bk%7D%7B4%5Cpi%5E2%20f%5E2%7D)
Now, plug in the given values and solve for 'm'. This gives,
![m=\frac{24200\ N/m}{4\pi^2\times (0.429\ Hz)^2 }\\\\m=\frac{24200\ N/m}{4\pi^2\times 0.184\ Hz^2}\\\\m\approx3331.5\ kg](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B24200%5C%20N%2Fm%7D%7B4%5Cpi%5E2%5Ctimes%20%280.429%5C%20Hz%29%5E2%20%7D%5C%5C%5C%5Cm%3D%5Cfrac%7B24200%5C%20N%2Fm%7D%7B4%5Cpi%5E2%5Ctimes%200.184%5C%20Hz%5E2%7D%5C%5C%5C%5Cm%5Capprox3331.5%5C%20kg)
Therefore, the mass of the truck is 3331.5 kg.
Answer: B) Solid water to liquid water.
Explanation: This would be the melting of water or a transition of solid water to liquid water as energy is added.
Answer:
Final temperature of the copper is 59 degrees Celsius
Explanation:
It is given that,
Mass of the sample of copper metal, m = 6.5 g
Initial temperature of the metal, ![T_i=25^{\circ}\ C=298\ K](https://tex.z-dn.net/?f=T_i%3D25%5E%7B%5Ccirc%7D%5C%20C%3D298%5C%20K)
Heat generated, Q = 84 J
The specific heat capacity of liquid water is 0.38 J/g-K
Let
is the final temperature of the copper. It can be calculated using the definition of specific heat of any substance. It is given by :
![Q=mc\Delta T](https://tex.z-dn.net/?f=Q%3Dmc%5CDelta%20T)
![Q=mc(T_f-T_i)](https://tex.z-dn.net/?f=Q%3Dmc%28T_f-T_i%29)
![T_f=\dfrac{Q}{mc}+T_i](https://tex.z-dn.net/?f=T_f%3D%5Cdfrac%7BQ%7D%7Bmc%7D%2BT_i)
![T_f=\dfrac{84}{6.5\times 0.38}+298](https://tex.z-dn.net/?f=T_f%3D%5Cdfrac%7B84%7D%7B6.5%5Ctimes%200.38%7D%2B298)
![T_f=332\ K](https://tex.z-dn.net/?f=T_f%3D332%5C%20K)
or
![T_f=59^{\circ}C](https://tex.z-dn.net/?f=T_f%3D59%5E%7B%5Ccirc%7DC)
So, the final temperature of the copper is 59 degrees Celsius. Hence, this is the required solution.
Answer:
5km/h
Explanation:
The equation for average speed is
Vavg = Δd/Δt
where Δd is distance and Δt is time
from what's given, we know she travelled 15km in total and the trip took 3 hours in total. We can now plug in the values into the equation
Vavg = 15/3
Vavg = 5km/h