Practice Free Response
1. A 0.62-kg block is attached to the spring (k = 180 N/m). When the system is compressed 5.0 cm and released, it slides a total of 7.3 cm before turning back.
What is the coefficient of friction?
2
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)
. Block with mass
M slides down and strikes
a smaller block with mass m, where
M = 3
m. The blocks stick and fall to the floor.
How far horizontally from the table's edge do the blocks land?
3. The force acting on an object along the
x axis varies as shown.
Fx (N)
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400
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200
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0
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x (m)
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1
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3
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5
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7
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9
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11
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13
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15
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-200
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Determine the work done by this force to move the object
a. from x = 0 to x = 10 m
b. from
x = 0 to
x = 15 m
4
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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUcAAACoCAIAAAD8TrvfAAAZuUlEQVR4nO2df0xV9f/Hz+jD5kBWM8hgDGNLfqSjGPFHa5LaFFNMwRoT0NnmpK1mIrM/wNRUoGUGay6Ftf5A/LXxY4Y/oDUjyFYJ2dqIH2smzGEOxmSAy7HR9/k9z/ne6XKhC9zLPefN6/HH2fu+77nnvO/7fZ7v1/t13r/+988//xiCIGjE//ydAEEQvIyoWhB0Q1QtCLohqhYE3RBVC4JuiKoFQTdE1YKgG6JqQdANUbUg6IaoWhB0Q1QtCLohqhYE3RBVC4JuiKoFQTdE1YKgG6Jqh9HR0dHS0qI+jo6OdnZ2IpCUlOS/RHmHXbt2NTU1IZCenv7000/79F5//fXXN998o0GmuUVU7TDiTdTH2tra3t5ew5SE/xLlZVatWlVYWOjTWxQVFfn0+v5FVO1soGqa7tLSUn+nRbALompn09jYODAwYJgtc6sNF+Yzompn09/fX1FRYZgtc3+nRbALompB0A1RtSDohqhaEHRDVC0IuiGqFmzHwMBAW1ubr2/h0+v7F1G1YCPCw8MN833+FKoeHR1V/XmhoaE4LlmyBD+MiIjw/Ea4BX9LamtrPdd5c3NzSkqK5/cy5nyMkKhasBGxsbE4lpeXu/0WUi8tLW1paYFIVpgEBwd75b4ZGRmen1xVVZWamoqqxCu39gWiasEB5OXl4XjlypUPPvgAovJjSvr6+lCtoLFg5yG6omrB7nR0dDQ0NCDQ2toaEhLCyP7+fsRzZstEkpKSVOPcu4k5d+4cjkiPqFoQZg58YLaQ0T7ft28fHGC4wWFhYZCu2xF1cLwrKip6enoMs0aIjo4+fPjwdD3hydi6devg4GBOTo5XruYjRNWCA6BhRLu3rKzswYMH8KihK6h6MlMMMVPVcMUrKyvxQ2+pOiIiAje1+fhcUbUg6IaoWrA7cKFpaUtKSrKystDAbjFBM3uy7qioqCg00Q3Twf7qq6/4an3+IKoW7M6YiWG2fnEMDg6Gq9ze3h4YGDg8PIyY7u5udXJ4eHhMTAxc34SEBH5cvHixnxLuN0TVgt2BmM+fP4/A3r17g4KC4FeHhobCtd63bx/9aqt3DXcaBhzmnUvEXLhwITc3F2eyb2yeIKoWHAAl2tfXl5mZCd22tbVB2GxjGxOGf3Z0dED5HJ3GH6oz5wmiasHuQKVcZqy1tVUNC21uboZu9+/fjzA0bD0fTvW6deuys7MNs1dsvknaEFUL9gfKZBs7Kyvr8OHD7K+GpCHXKfqrcTRMK52cnLx79247D/D0OqJqwQHU1NTg+IqJYS4t3NDQMLVQ4VrjWFdXd/z48ZGRkcnGlrulqalpw4YNaA44dGlhUbVgd2B1KWYcr169Sludm5sLB5uzO+Li4hhQL8nwE8ZAlgcPHty0adO07jg8PJyamupQSRuiasH+8J22YbbAw0xycnJgqNEI5wAyGGS61vCoVXOdmoTgExMTpzu169y5c9OaxWU3RNWC3YFKT5w4gcCrr766YsUKGNLu7u6NGzempaXFxMQY5uxodXJXV9fdu3f7+vrYiQ0HG+JH83takzGuXLkCC+/t/zF3iKoFQTdE1YIDYIfWs88+OzQ0hFZ3QkICmtaIjIyMdDkzNjZ2fHw8JCRkZGQEH2HbYbfZgPcQ2PbFixdzkClfpHtrbYY5Q1Qt2B3ImDMfT548uXLlSuPRjGu0rhEw3PVXw/eG7BFOTU3dt2/ftBY/QnsePjkHsZSWlhYVFcFv512ys7MdoXBRtWB31AJj9fX1y5Ytg7og6ZaWFr7ungikjq/4Ig2BwcHBTZs2eahGGGfrezJIuqqqilv5Qee46bp162b7f3yPqFqwOxBka2urYfZsnTp1CqpOT0+H3qae5ExVNzY2fvjhhzdu3PBwd0Hcy6VDy1p3TFaP2A1RteAAcnNzcVy4cGFNTQ37q2FRl5gY7vqr1aoJaIqnpaXt3LlzxreGZ063HEeEvfJ3fI2oWrA7kChMLgK3bt3iumVwsxHJcaOGueinS3813Gk2lZXgZwzuxVXTgoKCbL4EikJULdgdaImzO2JjYzMzMyHg5uZmRHKdI8Rbt7BXMzG5VSjOHB8fLykpmc2oEkf40lZE1YIDoK8bERHB8WSUdEpKCl90W60xzrTOxISBvXDhAl+Vzx9E1YLd6evr27hxIwKff/755s2bDfN19NmzZ/Pz8ylddk0rYmJiwsPDWREkJye/9957zzzzzNwn24+IqgVBN0TVDmB0dHT//v30IZ07kWjGBAYGPv7444ZltAkyZNGiRZGRkS5WWgEPfMGCBQjAqX748OGcJdUmiKodAPxGOJPzUM8kLCyM8ze2bdt25MiRgYEBZAXquIyMjMlWTejs7FTrgeMn27dvt75R0x5RtQPgaOTm5mYcz5w5M60FAPSAfUtwsN955x2oGh+rqqo6Ojr+s78aqo6Ojp5vFaKo2gE0NjbCKHFNbI5JnldAosXFxYalv7q0tBSihbCp9ry8PJf+agTmrcNiiKodQUtLC55RGh88r/5Ozlyj9tlatWrVnj17IGA0yOmSsAVu7U9mfzVMNKs/NHMSExPz8/PnlbxF1Q4AxgoPJX1LR8wZ8jpHjx7F8c0334RZhmizs7MLCgqm3jqLnV44Hjp0aPHixaJqwV5wZsK8ei6tqB15du7cefnyZdhquCQVFRV79+51ez4XLeMAFRjz8vLy1atXeysxuG9RURHXV/HWNb2OqNoBsJ05r9a+tTI2NjY+Pm6YKxwFm+SY+CUxTz31VG9v78KFC/1ydw8RVQt2JyIioqSkBIH169fD6hYWFvpxlsXmzZtDQ0PXrFnjrwR4gqhasBETd8MjbKfU19dXVVWhNc5ZWVPsX+0JM57OpSaE2RZRtSDohqhasBF8cf3WW28lJiZOdg6XLugwmfGNbt68WV1drV5A1tbWTrYV9kTQWOA0T8+Z1rrFs0dULdiO6OhoXy+yf//+fetHR6/pPxFRtWAjwsPDcVy6dGlLS4tPb4RbqEUO9UNULdgIrsJt565gRyCqFgTdEFULgm6IqgVBN0TVgqAbompB0A1RtSDohqhaEHRDVC0IuiGqFgTdEFULgm6IqgVBN0TVgqAbompB0A1RtSDohqhaEHRDVC0IuiGqFgTdEFULgm6IqgVBN0TVgqAbompB0A1RtSDohqhaEHRDVC0IuiGqFgTdEFU7m7a2tp6eHgRGR0dntm+roB+iakHQDVG1s8nIyOjt7TXMvVTFVgtEVO1soOqGhgYElixZ4u+0CHZBVO1sVq9eHRAQ4O9UCPZCf1XX1tbiODAw4NO7cDNkWM6+vr67d+/69F5WAgMDIyMjDfO1mSfnJyUl+ThFgv/RX9XFxcU4pqam+vQuFRUVhqlqn95lImEmc3xTwebor2ria701NjYyEGHi03sJwtTMF1ULwvxBVC0IuiGqFgTdEFULgm6IqgVBN0TVgqAbompB0A1fqbq/v7+urs5HF/eEuLi4lJQU9bGoqMiPiRGEucRXqg4LC9u1axfDnABcVlZWWlrqo9tNwenTp3F88OCB229HR0evXbt26dIlBFALREVFIeUc/jmt+RJBQUFeSa0gzJ65aIFzJDaOflF1fHy823ha75aWlu3bt1+9ehXhjo6Ozs5O49GgcTV0HGYfUp/sOoJgN+ZC1RxN2dvbC9nYRBt5eXkrVqxAAMeLFy9WVlbGm7id/NDW1oa/gMTzY0ZGRk5OzpwmVxCmw1yommOw2ay1CXD7q6qqDNOS5+fnj42NtT1i4slIOVrj+Bcw2obpSsDOFxYWznWiBcEz5kLVysG2iaEGwcHB9LRxzMrKSkxMhNFGOt360j0mDQ0N6pWbff6IIExknvZsjY6OcmEgWOB79+7Bu4a8YYQne6mGljnMOxvhED/db0GwJ/NU1YKgMe5VDfdyeHgYgZCQEC1XzxgfH4+JiUHgyJEjsNUff/wx/mZXV1d3d/fEk3FmbGxsX1/fuXPn8PHYsWPKpxAEG+Je1VFRUc899xwCt2/fntPkzBWorbiIX3l5eWVlJRxm+NVoV0+2qjYyBI1zdryjCkCLfa5TLAgeM6mt5ovrmS1Gi5/DC4VO8PSvW7duVgn0DUge2yC5ubmDg4PHjx9PT0+H23zmzBmXM4OCgvBVfHz8wMAATjbMXjGx1YKdca/qxsbG2Sz0BcGkpKTs2bPHtu+Kw8LCaKtPnz596tQpyLW2thb/mp1Y1jNRQ5WVleEfwVBzABnMO8fVCII9ca9qPPEFBQVT/xJPtnXhThfzFf+I2SfRF1ht9dDQEISKj/gLMNdoX/B/QcNIf3Z29hITNM65sCFsNSos/6ZfEKbAjaphlKwrVzY3N+OJx7M+Nja2ceNGddoU6/tBAJAEFAJ31J4bSuDfccBJYWHhhQsXqqqquGEV9Iw0U/D4F11dXYinvFERUO3SsyXYHDeqhhHGk82lcA1zdHRvby8a5FA1nv7/HCxJGw5rtm3bNrjW9lQ1FIv/aJgN7JCQkIiICCgZ6rX2VyPlsbGxDLO/mt8iQ2SjDMHOuFE1WpguMWimUsyw2P+pamXDYeS9kULfAvvc3t7+xhtvQNLQuVsjjPigRxjmrA9RtWBnPBqFEh4e7hJwOrDDN27cQODgwYPj4+PV1dVpaWmw2yMjIwsXLnQ5Ge1wGO3h4WG1T52HG2UIgl/wSNVwp2F4h4aGrH61o0ELPDo6GgHoGS3q7du3o40N6U6UK51qmGuY6Dt37himi6HlyBxBG2TEqCDohkeqZm9tYGCgNnvNoAVOs1xaWvrjjz8iDIuNv5mamjqxvxrHurq6/v5+dtThHOmvFuyMp7Z6Nu+HOLyMHV02GWqGSoovBYuLizdt2lRUVATFckicSyM8Li4OVUB2drbxaPmHioqK/+zMFwQ/MhctcK6X0Nvbax93NCcnh2PLampq2tvbq6qqUOnAhYaAKWOexnUU4IQbpnnn8in4iT276wSBzN1aKFC1ffZkhapZxcBij4+Pr1y5EjFsYEPeqtdaxnsLTmQuVg5G2DBfJquRLS7L+voUdptPNhqMyeA6JwMDAxQ2B6jAWZhuD5bUAoIdmIuVg/0Lp2GhFT3FqwG3Q9Y579JDvvzyS0NULdgDW/RsQXK+G1mtWgo+ur4V341OsXr7focD5v2dCvvCMQ5+TIAtVH3nzp38/Hyf3mJwcJBjSHwER4z77l+Ul5erQel+p7q6ur6+3t+psC8oKZSXHxNgC1UjF5qamvydCsFT8k38nQphUmyhakEQvIioWhB0Q1QtCLohqhYE3dBH1X19fTheu3YtNDT0wYMHbW1tft+zenR0lL3lEyeN6EptbS1yHv+3s7Nz69athrlIs/WEjo6OL774AoHjx4/P5kbMW66ZqfK2qqoqKioKCYiPj596xgFHSek6vkATVff09KxduxaB77//nuNS7bBkt5oZlpSUNE9Ujb9ZXFyM+hQVK7viWNsqoLdPP/3UmLWqmbcc9su8RX3R0NAAYSNSjWucDDwkHNU/M5qbm5EA+8xrcEETVaMs09LSDLO0GHP06FHDNB0s8qampuTkZHxb+AiuEwrxL1u2bM2aNdu2bUPF39jYmJGRwekouGZ0dPSmTZs44kIZ/9LS0pSUlPr6+szMTCVajnUxzKFssABxcXEIIF7tjzvfgKqVleZMOGQF8t+6QhZzj4vhwfYin3/77TfDXKUjKChounkLK43S5HalavZORUVFQkICWnB4HvAtV7MxzFGAOJN7qnMEFAsdkfgJLo74vLw8q24Rg4+4NWol1Fy4BfdItc/oIIUmqkZpuay+hLweHh6+fv0655agPFauXAltc+oYpE7949v8/PysrCw8UijFnTt3vvjii2fPnjXMCgL2BD/5888/8ZPPPvuMqka54rQdO3b88MMPf/zxx6FDh2COysrK8BXanA8fPsTPcX5MTAyOtl072Xcg25Fv0ORPP/3EmMrKSuQGSgRtb6uqkVEQcEBAAAIw7KiXFy1aZJhSfOWVV6x5y8b81HmL63/99devv/46DPW3337L8sURF8FdeLQOZKbCaXIRiXI3TFXjFviYmJio2gJkaGgItfmBAwdQC+D5wd1tqGeiiapRT6tqWNHd3T0yMqI+WsOTEWLichEYeRQnNx4DMPLLly8/ceIEzDgsPPy3mpoaztZcaWKYU8Hm7c71yEDk2MWLFx977DHGIA/ffvttaMDFj713757KMWQg1IgYfuWStzxn6rzFaagafvnlly1btkB71nMgzrt373qYftQsXV1df//99/r1663xqBRg2z15ivyOJqpGEb700kuGKTlW4axorQOzPfSCXE5DfQHjDFXjUmxxIaa1tfX5558/f/48ihmGBSewFYe2IqwBnC4057iOuhf/o4NAdsGd4Sp3ly9fZh5C0sgT61w9vtRELiGe28VERkYaZi2AeGveshE+dd6iUoCrDCvKRrj1K/zc871o0HyDdJFal4nDqE1wXzTZpp8fc40mqkZZotFlmI09lDqETXcaLhBXIwoMDCwoKIAnhoLv6enBc6a8NeW5wRPDc8bTDFO9aP7BXMAfy83Nzc7OZouL7+E++eQTw/QJcTtck4LHaS+//DLXNty/fz8eSnprtOTzAeQtcxi6GhsbM0yHBVUtcgaRqHyRt7TYCCjfFTHIeWRXZmamYYoQDpE1b7nD2cS8tWYs4vETnI9WW3l5Od+G4Kbwoe7cuYNiVbP3DHNmLs5Ub/L4YPDWeAxu3rwJYTNh6vp4qOhaQ9vp6ek4csaufVYNUGiiakEQFPqomv0oLn3UE9dmQHVrmBvxqBjVsakCtPPqo8s1XVp3hBW29Xa80Xwjw4ThQ4cOqXhYURW2zmdS6zquM2HYZYFq5K1LObrNW9hSa9HQVqMo6Y0b/579nmRijeQ1kR7+BZh0l85Rl2lYNlmBzy36qHo2cF9el3eegqOhV0U3yvO1ceF+FxcXw8l3aX47C1H1/wNrMD9Nq8bQlk7XogYHB/t9SOLsEVULgm44VdVqLY6pNwniFllev/vw8LDLYkYxMTE4qpbesIm14Yd2YFBQ0BNPPOH1xNgN/NPu7m5kiPXvM8fCw8OnLo7bt2/j+OSTT7qMGpgNv/766/379w2zu1stzuGSEpaXYSlBhY8eIZ/iSFWzgyElJSU3N3dqVVdXV3NkqHeHAXWbcEBSeXk55Hrt2jXD7DbnCR999NGSJUuUYwYf79133929e7d6c6MxEMb7779v/PsN2YEDBxoaGv5z/GxNTQ2O69ev9+KYvBdeeAFX47uugIAAdpK5pASlycUnXXZlR2R2dnZra6s1Er+1+ZBBR6p6YGCAI0OOHj0KwSCXEcONNVJN6urq2FGM3Oe7UKgaDxnk19LSgl/hI1cU7u3tTU5OtlbGLgNXOkzwq/T0dPUmNi4uzvpeDXfhEuJqj0FImtuDUOc4WfVqckQ0e0d1nfKBjIJ3ah3IjfxhxapWMkQmIHPUXkg4QlFs8jAzOU8DdQGHDBhmgwiFhcJFEVOWLBGcifjvvvsOuYozJ24RE2xiDRhmVYvSRwKgW7WNMePb29uhc8SzgPio4MqwEHjwkCTYFTuXnSNVXVBQsGXLFtpJCKysrAzPB4eFbNiwAcXDgfuG2QvF3A8MDEQkygNPFTXPEaZ4PpYvX37r1i2qDuWHR4rPBB6ykpISGhxUBK+99prakXui5ecrFtwU1jghIUGlk4+dquy5nyZqAe4HpPF+XRAA1zZDoxcVLhRCkeOP819z9BjyHzFo1ECQo6Ojly5dMsyKAMpEljLfICfuiLR06VI07/GRY7ArKipoM3Hmzz//zCcBjwTyfOJLMk4Rta4GjZLFrRGJX+E6tAr4IYw5Th4cHEQA50DkrMFxJp4c1CwI2FnShkNVjRJlfYky+P333yFI5DI9McgbcsUJLG9lIdEsRCROwxG6hfJZ2eNxgaFWp3FgI8O4OB4ylh9/NUWS2MDjOGHVU6o6WtW6yHh0eEENXrRODbLx2LFjhjliT208CE6fPs13ImzHImNR93HalmHZIB1ZF/wI41E1OnEsNwsO36L0VVXrtqRQR3MEMdVrmJUFSgeRqOKtCyFzuhgiKWamxPDgGbAPjlS1IAhT4EhVs2pn80lVvQStOE/2+kE1TFcNV+AAchWvxqLgUgjAv/IkSXwHA1vtdvQ/R4kb5iReGC60ArSfdw3LxvYLcgYNaTWjDh9PnjxpWAwv7ST957lModrO0aUs0MrgTB56SU7Ekaqmh8YpHOnp6dCn8ngNczgRxINzOPierhSadohE+XHIEV/SGGbRXrx4cffu3WwYo0FeXFzMq+G5hJN8/fp1wyx4CtKwtOpxZV4TDwefWjgFaAriAWWtgbsgeSphfG2+ZcsWfMUpRDZ/lTozkEvIQPjJ7J6AepFjqHyRV8gx5CprwGXLljFXAfQDlwRFwO6lfhNrebGw+FINWVdYWIgwql0WLoubYVUoKm+7urpUMfGOPI1dGCggNM6VsDkhNCAggNuhoqJR5c5jWloaF4Gw8zBER6pajQNTOUsHScVwHQzj32N3GcmhwniGVL8LnqSbN28q/1l5vLT5amixuqYCP1GR6n2YquBdLI9KiUs3iX5Aw9Y+Lb6nyDExJoymVvAVmnXZI2t5EWYd5OrS/8QzUfSMdymp2NhYFaOSwYSpdyi4JuP5CoDx+BXC6rcqJfZ/x+lIVVuBJlEZNzU1TavuXLBgAde+iImJWbt27Y4dO3yVPsFR4ME4a4K6QMaB+w20eGewm4/sKSO4ZWaPk91wvKoFQXBBVC0IuiGqFgTdEFULgm78H+WZNy9schqpAAAAAElFTkSuQmCC)
. Students are to
calculate the spring constant k of a spring that initially rests on a table. When the spring is compressed a distance
x from its uncompressed length
Lo and then released, the top rises to a maximum height
h above the point of maximum compression. The students repeat the experiment,
measuring h with various masses
m taped to the top of the spring
.
a. Derive an expression for the height h in terms of m, x, k, and fundamental constants.
With the spring compressed a distance
x = 0.020
m in each trial, the students obtained the data for different values of
m.
|
|
|
|
|
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m (kg)
|
0.020
|
0.030
|
0.040
|
0.050
|
0.060
|
h (m)
|
0.49
|
0.34
|
0.28
|
0.19
|
0.18
|
|
|
|
|
|
|
b. (1) What quantities should be graphed so that the slope of a best-fit straight line can be used to calculate the spring constant
k?
(2) Fill in one or both of the blank columns in the table with calculated values of your quantities.
c. On the axes below, plot your data and draw a best-fit straight line. Label the axes and indicate the scale.
d. Using your best-fit line, calculate the spring constant.
e. The height
h that the spring reaches is difficult to measure. How would you determine this value?