Answer:
a) 50μC
b) 37.45 m/s
Explanation:
a) If the spheres are connected the charge in both spheres tends to be equal. This because is the situation of minimum energy.
Thus, you have:
Hence, each sphere has a charge of 50μC.
b) You use the fact that the total work done by the electric force is equal to the change in the kinetic energy of the sphere. Then, you use the following equations:
![\Delta W=\Delta K\\\\\int_{0.4}^\infty Fdr=\frac{1}{2}m[v^2-v_o^2]\\\\F=k\frac{Q^2}{r^2}\\\\v_o=0m/s\\\\m=0.08kg\\\\kQ^2\int_{0.4}^{\infty} \frac{dr}{r^2}=kQ^2[-\frac{1}{r}]_{0.4}^{\infty}=\frac{kQ^2}{0.4m}=\frac{(8.98*10^9Nm^2/C^2)(50*10^{-6}C)^2}{0.4m}\\\\kQ^2\int_{0.4}^{\infty} \frac{dr}{r^2}=56.125J](https://tex.z-dn.net/?f=%5CDelta%20W%3D%5CDelta%20K%5C%5C%5C%5C%5Cint_%7B0.4%7D%5E%5Cinfty%20Fdr%3D%5Cfrac%7B1%7D%7B2%7Dm%5Bv%5E2-v_o%5E2%5D%5C%5C%5C%5CF%3Dk%5Cfrac%7BQ%5E2%7D%7Br%5E2%7D%5C%5C%5C%5Cv_o%3D0m%2Fs%5C%5C%5C%5Cm%3D0.08kg%5C%5C%5C%5CkQ%5E2%5Cint_%7B0.4%7D%5E%7B%5Cinfty%7D%20%5Cfrac%7Bdr%7D%7Br%5E2%7D%3DkQ%5E2%5B-%5Cfrac%7B1%7D%7Br%7D%5D_%7B0.4%7D%5E%7B%5Cinfty%7D%3D%5Cfrac%7BkQ%5E2%7D%7B0.4m%7D%3D%5Cfrac%7B%288.98%2A10%5E9Nm%5E2%2FC%5E2%29%2850%2A10%5E%7B-6%7DC%29%5E2%7D%7B0.4m%7D%5C%5C%5C%5CkQ%5E2%5Cint_%7B0.4%7D%5E%7B%5Cinfty%7D%20%5Cfrac%7Bdr%7D%7Br%5E2%7D%3D56.125J)
where you have used the Coulomb constant = 8.98*10^9 Nm^2/C^2
Next, you equal the total work to the change in K:
hence, the speed of the spheres is 37.45 m/s
Answer:
4
Explanation:
The weight of the rock is W = mg = (80 kg) (10 m/s²) = 800 N.
The mechanical advantage is therefore 800 N / 200 N = 4.
Answer:
The work required is -515,872.5 J
Explanation:
Work is defined in physics as the force that is applied to a body to move it from one point to another.
The total work W done on an object to move from one position A to another B is equal to the change in the kinetic energy of the object. That is, work is also defined as the change in the kinetic energy of an object.
Kinetic energy (Ec) depends on the mass and speed of the body. This energy is calculated by the expression:
where kinetic energy is measured in Joules (J), mass in kilograms (kg), and velocity in meters per second (m/s).
The work (W) of this force is equal to the difference between the final value and the initial value of the kinetic energy of the particle:
In this case:
- W=?
- m= 2,145 kg
- v2= 12
- v1= 25
Replacing:
W= -515,872.5 J
<u><em>The work required is -515,872.5 J</em></u>
Answer: C. 1.64 x 10-3 m/s2
Answer:
the reaction force in this situation would be B
Explanation:
The action is the wings pushing down whilst the reaction is the air pushing up which allow the bird to fly .
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