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什么是三角函数

$4. (18 pts) A 1.0 kg particle is released from rest at the origin $\vec{\mathbf{r}}_{0} = (0 \hat{\mathbf{i}} + 0 \hat{\mathbf{j}}) \mathrm{m}$ , and is then subject to a position-dependent force given in Newtons by \[\vec{\mathbf{F}} (x,y) = (y \hat{\mathbf{i}} -x \hat{\mathbf{j}}).\] Furthermore, the particle is constrained to a parabolic curve so that it only moves along the path \[y = 10x - x^{2}\] where both $x$ and $y$ are measured in meters. (a) Is this force conservative? How can you tell? (b) Calculate the work done by the force on the particle as it moves along the parabolic path to a final position $\vec{\mathbf{r}}_{f} = (10 \hat{\mathbf{i}} + 0 \hat{\mathbf{j}}) \mathrm{m}$ . (c) What is the speed of the particle after this displacement? 解题讲题$

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4. (18 pts) A 1.0 kg particle is released from rest at the origin $\vec{\mathbf{r}}_{0} = (0 \hat{\mathbf{i}} + 0 \hat{\mathbf{j}}) \mathrm{m}$ , and is then subject to a position-dependent force given in Newtons by \[\vec{\mathbf{F}} (x,y) = (y \hat{\mathbf{i}} -x \hat{\mathbf{j}}).\] Furthermore, the particle is constrained to a parabolic curve so that it only moves along the path \[y = 10x - x^{2}\] where both $x$ and $y$ are measured in meters. (a) Is this force conservative? How can you tell? (b) Calculate the work done by the force on the particle as it moves along the parabolic path to a final position $\vec{\mathbf{r}}_{f} = (10 \hat{\mathbf{i}} + 0 \hat{\mathbf{j}}) \mathrm{m}$ . (c) What is the speed of the particle after this displacement? 解题讲题

$A $0.25 \mathrm{kg}$ block is released from rest on a frictionless ramp from a height of $1.40 \mathrm{m}$ above the ground. At the bottom of the ramp at ground level the block runs into and compresses a spring with spring constant $k = 2.0 \mathrm{N / cm}$ . (a) How far does the spring compress upon the block's collision? (b) How far would the spring compress if instead the block were to lose $40\%$ of its original mechanical energy due to friction with the ramp? 使用 mathtex 显示公式$

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A $0.25 \mathrm{kg}$ block is released from rest on a frictionless ramp from a height of $1.40 \mathrm{m}$ above the ground. At the bottom of the ramp at ground level the block runs into and compresses a spring with spring constant $k = 2.0 \mathrm{N / cm}$ . (a) How far does the spring compress upon the block's collision? (b) How far would the spring compress if instead the block were to lose $40\%$ of its original mechanical energy due to friction with the ramp? 使用 mathtex 显示公式

$A $40 \mathrm{kg}$ crate is pushed at constant velocity a distance $10.0 \mathrm{m}$ along a $30^{\circ}$ incline by the horizontal force $\bar{\mathbf{F}}$ . The coefficient of kinetic friction between the crate and the incline is $\mu_{k} = 0.25$ . Calculate the work done by (a) the applied force, (b) the frictional force, (c) the gravitational force, and (d) the net force.$

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A $40 \mathrm{kg}$ crate is pushed at constant velocity a distance $10.0 \mathrm{m}$ along a $30^{\circ}$ incline by the horizontal force $\bar{\mathbf{F}}$ . The coefficient of kinetic friction between the crate and the incline is $\mu_{k} = 0.25$ . Calculate the work done by (a) the applied force, (b) the frictional force, (c) the gravitational force, and (d) the net force.

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什么是张力

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演示动能和势能是如何转换的

$1. (12 pts) Caroline takes her baby sister Hannah to the neighborhood park and places her in the seat of the children's swing. Caroline pulls the $L = 1.8 \mathrm{m}$ long chain back to make an angle $\theta = 26^{\circ}$ with respect to the vertical and lets $14 \mathrm{kg}$ Hannah (swing mass included) go. (a) Determine Hannah's speed at the lowest point in the trajectory. (b) What is the tension in the swing chain at this low point? Assume the chain itself has negligible mass.$

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1. (12 pts) Caroline takes her baby sister Hannah to the neighborhood park and places her in the seat of the children's swing. Caroline pulls the $L = 1.8 \mathrm{m}$ long chain back to make an angle $\theta = 26^{\circ}$ with respect to the vertical and lets $14 \mathrm{kg}$ Hannah (swing mass included) go. (a) Determine Hannah's speed at the lowest point in the trajectory. (b) What is the tension in the swing chain at this low point? Assume the chain itself has negligible mass.

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14、感谢记忆！（奈瑟的“自传体记忆”研究）主要内容：研究了人们对个人生活中重大事件的记忆（“闪光灯记忆”），发现尽管当事人对这类记忆的信心很高，但它们同样会随着时间推移而扭曲和遗忘，并非我们想象的那么精确。

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你所看到的就是你所记住的（洛夫特斯的“误导信息效应”研究）主要内容：通过实验证明，在事件发生后提供的误导性信息，可以改变甚至植入人们对事件的记忆。这项研究对目击者证词的可靠性提出了根本性质疑，并对司法领域产生了深远影响。

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Video History

什么是三角函数

什么是张力

演示动能和势能是如何转换的

2cos(3t)的导数是什么?

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