If the K.E of a body increases by 400j. What would be its percentage increasing in momentum?
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KE is increased by 400 Joules.
![KE=\frac{P^2}{2m},\ \ \ P=\sqrt{2m*KE}\\\\P_2-P1=\sqrt{2m}(\sqrt{KE_2}-\sqrt{KE_1})\\\\ \frac{P_2-P1}{P1}=\frac{(\sqrt{KE_2}-\sqrt{KE_1})}{\sqrt{KE_1}}=\sqrt{\frac{KE_2}{KE_1}}-1\\\\ \%increase\ in\ momentum=100*\ [ \sqrt{\frac{KE_1+400}{KE_1}} - 1]\\\\=100*\ [ \sqrt{1+\frac{400}{KE_1}} - 1]](https://tex.z-dn.net/?f=KE%3D%5Cfrac%7BP%5E2%7D%7B2m%7D%2C%5C+%5C+%5C+P%3D%5Csqrt%7B2m%2AKE%7D%5C%5C%5C%5CP_2-P1%3D%5Csqrt%7B2m%7D%28%5Csqrt%7BKE_2%7D-%5Csqrt%7BKE_1%7D%29%5C%5C%5C%5C+%5Cfrac%7BP_2-P1%7D%7BP1%7D%3D%5Cfrac%7B%28%5Csqrt%7BKE_2%7D-%5Csqrt%7BKE_1%7D%29%7D%7B%5Csqrt%7BKE_1%7D%7D%3D%5Csqrt%7B%5Cfrac%7BKE_2%7D%7BKE_1%7D%7D-1%5C%5C%5C%5C+%5C%25increase%5C+in%5C+momentum%3D100%2A%5C+%5B+%5Csqrt%7B%5Cfrac%7BKE_1%2B400%7D%7BKE_1%7D%7D+-+1%5D%5C%5C%5C%5C%3D100%2A%5C+%5B+%5Csqrt%7B1%2B%5Cfrac%7B400%7D%7BKE_1%7D%7D+-+1%5D "KE=\frac{P^2}{2m},\ \ \ P=\sqrt{2m*KE}\\\\P_2-P1=\sqrt{2m}(\sqrt{KE_2}-\sqrt{KE_1})\\\\ \frac{P_2-P1}{P1}=\frac{(\sqrt{KE_2}-\sqrt{KE_1})}{\sqrt{KE_1}}=\sqrt{\frac{KE_2}{KE_1}}-1\\\\ \%increase\ in\ momentum=100*\ [ \sqrt{\frac{KE_1+400}{KE_1}} - 1]\\\\=100*\ [ \sqrt{1+\frac{400}{KE_1}} - 1]")
If you know the momentum, or velocity or mass then you can numerically calculate it.
If you know the momentum, or velocity or mass then you can numerically calculate it.
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