#170 The dimensions of the quantity kinetic energy
The dimensions of the quantity kinetic energy - Physics
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The dimensions of the quantity kinetic energy, designated by K, are kg · m2/s2. It can be written in terms of the momentum p and mass m as K = p2/2m.A. What are the units of momentum in terms of fundamental SI units? (Use the following as necessary: kg, m, and s.)
B. Force is measured in units of newtons, N, where 1 N = 1 kg · m/s2. What are the units of momentum p in terms of a newton and another fundamental SI unit? (Use the following as necessary: N, m, and s.)
C. What If? Physicists often measure the momentum of subatomic particles moving near the speed of light in units of MeV/c, where c is the speed of light, and 1 Me V= 1.6 ✕ 10−13 kg · m2/s2.Based on this, what are the units of momentum for a high-speed subatomic particle in terms of fundamental SI units?
D. What are the units of momentum for a high-speed subatomic particle in terms of a newton and another fundamental SI unit?
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(A) From the given expression of kinetic energy in terms of momentum,
For unit calculation,
![[p]=\sqrt{[2]\times [m]\times [K]}=\sqrt{1\times kg\times kg\times m^2/s^2}=kg.m/s](https://blogger.googleusercontent.com/img/proxy/AVvXsEhQ5DmY3PZnEIeT_-5dDSdcQmI-ioqrSdPWT2BS-rYjqrDzHAvpHFow0jlaA2Er4OjAfmDhNVR30vKag1ln30e99JPbYCilW18DjJtvLW9qWntUUnJ_taPf87axoy9_mOLNiwk1lcmQB91fR7YNLLO4jbwdrWSrVlDHI4epJUS0HMf0n1HH3D_wbOy1eQvnfhLx01GYE1AfmFM3uDXZ8PtHATcEBphEDM0Fos4ZQpp6fMY7e8vBapSM=s0-d-e1-ft)
(B) Momentum in term of force can be given as
![\Delta p=F\Delta t\Rightarrow [\Delta p]=[F]\times[\Delta t]\\ \Rightarrow [p]=N \times s=N.s](https://blogger.googleusercontent.com/img/proxy/AVvXsEgnYmdIevi2vMJFzJs7E1bxedyQPz6C8UK1ANMS92D9sq5tPQW0ZzYiKztdOSsYOOtxNApfrV3tLFTSCX8-XFEzOKEn__toTO1mOsGlyoJiUtB5mmZL_eWXsqvOSH0g-rDsY2nu8l4x3mye4bygIB7R09ai4njkz2gNv5Q_gygbQDTnAd86MOmGrb35hq8Z4BSX3fspMObJLMYVlP-J1AiSC2Wq0Ztl0BACLaZp19TKkNoKG8r1t2dq=s0-d-e1-ft)
(C) Unit of momentum in fundamental SI unit can be calculated as
![[\Delta p]=[$MeV/c$]=\frac{[e]\times[V]}{[c]}=\frac{C\times N/C\times m}{m/s}\\ \Rightarrow [p]=N.s.=kg.m/s](https://blogger.googleusercontent.com/img/proxy/AVvXsEgEsEyLgFfLepfE216ZUxryNkv89W87Zs3QAJ3RlvI6vIwb8Ix1cowU1U-I95C-C0SV6p4s7Oc-MFZd7-ZlIPMeLRgRF8qppP88F6G9QxGi4YJLt9RobdSBved40MH8J5I2ffiRqIS8pgqHBWXriYDxrCST7VD02DHa0fVV71FJiALiWXQXUfQxaZ4CZoKTzBPI0sOHyDsNhriozUs8aPc2uSWfc9EJBwz5si7VqATDHTIi1mIqv3dM=s0-d-e1-ft)
(D) In terms of Newton, it already has done in previous part
![[p]=N.s.](https://blogger.googleusercontent.com/img/proxy/AVvXsEhtio9SUS5TSNtuKaok0nRLwOYeNh6SOjcd_stnrdeQuBJF8Y3Qrm5q-9T5GybaGP-vXVRX56THswyRGZIaArFolY5g4HEqibFO3OTWt9LXpRU64iixTfBIlYEnIwkSzDep0KKT8IiSMRuLavfbm-pdslxSSe6_v5bVErXtnpUFftxWqgc0L0hf_AD1okPczSlENC1-JUrWEZhXKD0uCdKkoeYre2-KFAUY_D86L1mLgXOpc9I9qa1I=s0-d-e1-ft)
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