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(II) The momentum of a particle, in SI units, is given by $\vec{\mathbf{p}}=$ $4.8 t^{2} \hat{\mathbf{i}}-8.0 \hat{\mathbf{j}}-8.9 t \hat{\mathbf{k}}$ . What is the force as a function of time?

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$F=9.6 t \widehat{i}-8.9 \widehat{k}$

Physics 101 Mechanics

Chapter 9

Linear Momentum

Motion Along a Straight Line

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

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September 12, 2021

a boy stand on a vertical cliff 90m high,is whirling a stone of mass 500g attched in a string of length 50cm and maxximum withstanding tension of 630N.the string sweeps a vertical circle and break at its expected breakage point in the circle.If the stone

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Okay, so we're doing Chapter nine Problem. Three year. And this problem says the momentum of a particle given an S I units is the momentum vector. And it is a 4.8 t squared in the eye. Heart corruption minus 8.0 in the J hat. You're minus eight groups. Maya's 8.9 times t me que ha direction. Okay. And it says, what is the force as a function of time? Okay, well, we should know that the force specter here is given by the time derivative or the retributive of the momentum expected time. So we can just take our vector here. Think kind derivative of it. Coordinate t squared. I read as eight J mice, you 80.9 g k cool. So let's just differentiate this in the first part. You're just in power will be get 9.8 times to tea. So that comes out to being I just never realized. Um, back is not 9.8. That was 4.8, but we couldn't even tell because my terrible he and driving. So let me fix that real fast. Okay, so we have 4.8. He squared, so 4.8 times two times t. So 4.8 times two is 9.6. We have a tea left over in this point is in the eye direction. Cool. And now the J component. There's no tea here, So the time derivative of eight is just zero. Okay. And now in the cake compartment, we have eight point negative. 8.9 t. So driven. That is just negative. 0.9 in the K had direction. And this is our force factor as a function of time. Good.

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