Answer:
![\dfrac{1}{16}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B16%7D)
![\dfrac{5}{3}](https://tex.z-dn.net/?f=%5Cdfrac%7B5%7D%7B3%7D)
Explanation:
= Mass of first object
= Mass of second object
v = Speed of both objects
= Combined velocity
The ratio of final kinetic energy to initial kinetic energy will be
![\dfrac{K_f}{K_i}=\dfrac{\dfrac{1}{2}(m_1+m_2)(\dfrac{v}{4})^2}{\dfrac{1}{2}(m_1v^2+m_2v^2)} \\\Rightarrow \dfrac{K_f}{K_i}=\dfrac{(m_1+m_2)\dfrac{v^2}{16}}{m_1v^2+m_2v^2}\\\Rightarrow \dfrac{K_f}{K_i}=\dfrac{(m_1+m_2)\dfrac{1}{16}}{m_1+m_2}\\\Rightarrow \dfrac{K_f}{K_i}=\dfrac{1}{16}](https://tex.z-dn.net/?f=%5Cdfrac%7BK_f%7D%7BK_i%7D%3D%5Cdfrac%7B%5Cdfrac%7B1%7D%7B2%7D%28m_1%2Bm_2%29%28%5Cdfrac%7Bv%7D%7B4%7D%29%5E2%7D%7B%5Cdfrac%7B1%7D%7B2%7D%28m_1v%5E2%2Bm_2v%5E2%29%7D%20%5C%5C%5CRightarrow%20%5Cdfrac%7BK_f%7D%7BK_i%7D%3D%5Cdfrac%7B%28m_1%2Bm_2%29%5Cdfrac%7Bv%5E2%7D%7B16%7D%7D%7Bm_1v%5E2%2Bm_2v%5E2%7D%5C%5C%5CRightarrow%20%5Cdfrac%7BK_f%7D%7BK_i%7D%3D%5Cdfrac%7B%28m_1%2Bm_2%29%5Cdfrac%7B1%7D%7B16%7D%7D%7Bm_1%2Bm_2%7D%5C%5C%5CRightarrow%20%5Cdfrac%7BK_f%7D%7BK_i%7D%3D%5Cdfrac%7B1%7D%7B16%7D)
The ratio is ![\dfrac{1}{16}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B16%7D)
As the linear momentum is conserved
![m_1v-m_2v=(m_1+m_2)\dfrac{v}{4}\\\Rightarrow m_1-m_2=(m_1+m_2)\dfrac{1}{4}](https://tex.z-dn.net/?f=m_1v-m_2v%3D%28m_1%2Bm_2%29%5Cdfrac%7Bv%7D%7B4%7D%5C%5C%5CRightarrow%20m_1-m_2%3D%28m_1%2Bm_2%29%5Cdfrac%7B1%7D%7B4%7D)
Divide by
on both sides
![\dfrac{m_1}{m_2}-1=\dfrac{m_1}{4m_2}+\dfrac{1}{4}\\\Rightarrow \dfrac{m_1}{m_2}-\dfrac{m_1}{4m_2}=\dfrac{1}{4}+1\\\Rightarrow \dfrac{3m_1}{4m_2}=\dfrac{5}{4}\\\Rightarrow \dfrac{m_1}{m_2}=\dfrac{5\times 4}{3\times 4}\\\Rightarrow \dfrac{m_1}{m_2}=\dfrac{5}{3}](https://tex.z-dn.net/?f=%5Cdfrac%7Bm_1%7D%7Bm_2%7D-1%3D%5Cdfrac%7Bm_1%7D%7B4m_2%7D%2B%5Cdfrac%7B1%7D%7B4%7D%5C%5C%5CRightarrow%20%5Cdfrac%7Bm_1%7D%7Bm_2%7D-%5Cdfrac%7Bm_1%7D%7B4m_2%7D%3D%5Cdfrac%7B1%7D%7B4%7D%2B1%5C%5C%5CRightarrow%20%5Cdfrac%7B3m_1%7D%7B4m_2%7D%3D%5Cdfrac%7B5%7D%7B4%7D%5C%5C%5CRightarrow%20%5Cdfrac%7Bm_1%7D%7Bm_2%7D%3D%5Cdfrac%7B5%5Ctimes%204%7D%7B3%5Ctimes%204%7D%5C%5C%5CRightarrow%20%5Cdfrac%7Bm_1%7D%7Bm_2%7D%3D%5Cdfrac%7B5%7D%7B3%7D)
The ratio of mass is ![\dfrac{5}{3}](https://tex.z-dn.net/?f=%5Cdfrac%7B5%7D%7B3%7D)
Answer:
B = 0.088 T
Explanation:
Given that,
The length of a solenoid, l = 0.4 m
No. of turns of wire, N = 356
Current, I = 79 A
We need to find the magnitude of the magnetic field at the center of the solenoid. It is given by the formula.
![B=\mu_onI\\\\B=\mu_o \dfrac{N}{l}\times I\\\\B=4\pi \times 10^{-7}\times \dfrac{356}{0.4}\times 79\\\\B=0.088\ T](https://tex.z-dn.net/?f=B%3D%5Cmu_onI%5C%5C%5C%5CB%3D%5Cmu_o%20%5Cdfrac%7BN%7D%7Bl%7D%5Ctimes%20I%5C%5C%5C%5CB%3D4%5Cpi%20%5Ctimes%2010%5E%7B-7%7D%5Ctimes%20%5Cdfrac%7B356%7D%7B0.4%7D%5Ctimes%2079%5C%5C%5C%5CB%3D0.088%5C%20T)
So, the magnitude of the magnetic field at the center of the solenoid is 0.088 T.
Answer:
toward the ceiling
Explanation:
In order to determine the direction of the magnetic force on the charge, we should use the right-hand rule. Putting the thumb, the index finger and the middle finger of the right hand perpendicular to each other, we have: (for a positive charge)
- The index finger corresponds to the direction of motion of the charge (in this case, toward north)
- The middle finger corresponds to the direction of the magnetic field (in this case, towards west)
- The thumb will give us the direction of the magnetic force --> in this case, the thumb points towards the ceiling, so the direction of the magnetic force is towards the ceiling.
Answer:
The best single equation in order to fin the acceleration is
![a=v_f/t=250/2=125m/s^2](https://tex.z-dn.net/?f=a%3Dv_f%2Ft%3D250%2F2%3D125m%2Fs%5E2)
Explanation:
The best single equation in order to find the acceleration is the following kinematics equation:
![v_f=v_o+at](https://tex.z-dn.net/?f=v_f%3Dv_o%2Bat)
As the rocket start from the rest, the initial velocity value is zero. Then the acceleration value is:
![a=v_f/t=250/2=125m/s^2](https://tex.z-dn.net/?f=a%3Dv_f%2Ft%3D250%2F2%3D125m%2Fs%5E2)
Experimental research is a method for picking up learning by methods for coordinate perception or experience. Exact confirmation can be broke down quantitatively or subjectively. Through measuring the proof or comprehending it in subjective frame, a scientist can answer exact inquiries, which ought to be unmistakably characterized and liable with the confirmation gathered. Research configuration fluctuates by field and by the inquiry being examined.