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$\bullet$ Some useful relationships. The following relationshipsbetween the momentum and kinetic energy of an object can bevery useful for calculations: If an object of mass $m$ hasmomentum of magnitude $p$ and kinetic energy $K,$ show that (a) $K=\left(p^{2} / 2 m\right),$ and $(b) p=\sqrt{2 m K}$ . (c) Find the momen-tum of a 1.15 kg ball that has 15.0 J of kinetic energy. (d) Findthe kinetic energy of a 3.50 kg cat that has 0.220 $\mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$ ofmomentum.

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a) $K=\frac{p^{2}}{2 \mathrm{m}}$b) $p=\sqrt{2 m K}$c) 5.88 $\mathrm{kg} \mathrm{m} / \mathrm{s}$d) $6.9 \times 10^{-3} \mathrm{J}$

Physics 101 Mechanics

Chapter 8

Momentum

Physics Basics

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Cornell University

University of Michigan - Ann Arbor

University of Washington

Lectures

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in this problem in far way. We need to show the relation. Okay, Is a little peace square by toe. Now, in this case is the chaotic energy. He is the Wyndham at M is the mass. Of course he is the magnitude of the moment. No, we know that momentum is mass Times velocity. Where is the magnitude of velocity? No, From this we can say velocity is more. Went on by mass. Now we know that kind of energy is half empty square. So now it is such a duty Expression for velocity. Here we get half and mass multiplied by the last day which is key by am all square. Just have him. He's whereby am square so we can sell him on Beget Alec energy. Is he squared by to em now for five are being We need to show he is through Tokyo. This is simple because we already have the previous expression. Okay, is equal to the square by two m if we send it to him to the other side are multiplying vortex. But I'm bigger. He's square is to em. Okay, which means the mountain is simply he The morning p simply the square off too. Now for party, we're given the mask. The mask off an object is 1.15 kilograms on the kind of energy is 100 15.0. Jules, we need to find out p now. We simply used the second relation. That just fruit p is it called a route? Okay, so the morning p is simply squared off two times higher Technology, which is 15. Jules multiplied by mass, which is 1.15 kilograms. Excuse. 5.87 kilogram meters. Now for five d, we have given the momentum often object. Is there a 1 to 0? Which a person, a debate over second and the mask is 3.5 and we want to find out the kind of energy for this We simply is the first expression. Be proved. Okay, is a little peace queer wayto which is they want to square you wanted by two times 3.5. This turns out to be 6.91 times and by minus three jewels. This is the kind of energy of the object

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