Answer:
(a) 7.72×10⁵ J
(b) 4000 J
(c) 1.82×10⁻¹⁶ J
Explanation:
Kinetic Energy: This can be defined energy of a body due to its motion. The expression for kinetic energy is given as,
Ek = 1/2mv²................... Equation 1
Where Ek = Kinetic energy, m = mass, v = velocity
(a)
For a moving automobile,
Ek = 1/2mv².
Given: m = 2.0×10³ kg, v = 100 km/h = 100(1000/3600) m/s = 27.78 m/s
Substitute into equation 1
Ek = 1/2(2.0×10³)(27.78²)
Ek = 7.72×10⁵ J
(b)
For a sprinting runner,
Given: m = 80 kg, v = 10 m/s
Substitute into equation 1 above,
Ek = 1/2(80)(10²)
Ek = 40(100)
Ek = 4000 J
(c)
For a moving electron,
Given: m = 9.10×10⁻³¹ kg, v = 2.0×10⁷ m/s
Substitute into equation 1 above,
Ek = 1/2(9.10×10⁻³¹)(2.0×10⁷)²
Ek = 1.82×10⁻¹⁶ J
Answer:
Explanation:
<u></u>
<u>1. Formulae:</u>
Where:
- E = kinetic energy of the particle
- λ = de-Broglie wavelength
- m = mass of the particle
- v = speed of the particle
- h = Planck constant
<u><em>2. Reasoning</em></u>
An alha particle contains 2 neutrons and 2 protons, thus its mass number is 4.
A proton has mass number 1.
Thus, the relative masses of an alpha particle and a proton are:
![\dfrac{m_\alpha}{m_p}=4](https://tex.z-dn.net/?f=%5Cdfrac%7Bm_%5Calpha%7D%7Bm_p%7D%3D4)
For the kinetic energies you find:
![\dfrac{E_\alpha}{E_p}=\dfrac{m_\alpha \times v_\alpha^2}{m_p\times v_p^2}](https://tex.z-dn.net/?f=%5Cdfrac%7BE_%5Calpha%7D%7BE_p%7D%3D%5Cdfrac%7Bm_%5Calpha%20%5Ctimes%20v_%5Calpha%5E2%7D%7Bm_p%5Ctimes%20v_p%5E2%7D)
![\dfrac{1eV}{4eV}=\dfrac{4\times v_\alpha^2}{1\times v_p^2}\\\\\\\dfrac{v_p^2}{v_\alpha^2}=16\\\\\\\dfrac{v_p}{v_\alpha}=4](https://tex.z-dn.net/?f=%5Cdfrac%7B1eV%7D%7B4eV%7D%3D%5Cdfrac%7B4%5Ctimes%20v_%5Calpha%5E2%7D%7B1%5Ctimes%20v_p%5E2%7D%5C%5C%5C%5C%5C%5C%5Cdfrac%7Bv_p%5E2%7D%7Bv_%5Calpha%5E2%7D%3D16%5C%5C%5C%5C%5C%5C%5Cdfrac%7Bv_p%7D%7Bv_%5Calpha%7D%3D4)
Thus:
![\dfrac{m_\alpha}{m_p}=4=\dfrac{v_p}{v__\alpha}](https://tex.z-dn.net/?f=%5Cdfrac%7Bm_%5Calpha%7D%7Bm_p%7D%3D4%3D%5Cdfrac%7Bv_p%7D%7Bv__%5Calpha%7D)
![m_\alpha v_\alpha=m_pv_p](https://tex.z-dn.net/?f=m_%5Calpha%20v_%5Calpha%3Dm_pv_p)
From de-Broglie equation, λ = h/(mv)
![\dfrac{\lambda_p}{\lambda_\alpha}=\dfrac{m_\lambda v_\lambda}{m_pv_p}=\dfrac{1}{1}=1:1](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Clambda_p%7D%7B%5Clambda_%5Calpha%7D%3D%5Cdfrac%7Bm_%5Clambda%20v_%5Clambda%7D%7Bm_pv_p%7D%3D%5Cdfrac%7B1%7D%7B1%7D%3D1%3A1)
If each mL has 30 grams of the substance in it, then 60 mL have 1800 grams of mass in them. the weight of 1,800 grams of mass on Earth is (1.8 kg) x (9.8 m/s^2) = 17.6 newtons.