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MechanicsQuestion and Answers: Page 10

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If there is a positive error in the measurement of velocity of a body, then the error in the measure- ment of kinetic energy is

$$\mathrm{If}\:\mathrm{there}\:\mathrm{is}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{error}\:\mathrm{in}\:\mathrm{the}\:\mathrm{measurement} \\ $$$$\mathrm{of}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{a}\:\mathrm{body},\:\mathrm{then}\:\mathrm{the}\:\mathrm{error}\:\mathrm{in}\:\mathrm{the}\:\mathrm{measure}- \\ $$$$\mathrm{ment}\:\mathrm{of}\:\mathrm{kinetic}\:\mathrm{energy}\:\mathrm{is} \\ $$

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A=(n−10)×(n−10) det(A)=?

$${A}=\left({n}−\mathrm{10}\right)×\left({n}−\mathrm{10}\right) \\ $$$${det}\left({A}\right)=?\: \\ $$

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∫e^(sinx) xdx=?

$$\int{e}^{\mathrm{sin}{x}} \:{xdx}=? \\ $$

Question Number 121123 Answers: 1 Comments: 0

two cars moving at speed of 10(m/(sec)) and 16(m/(sec)) on a road with a length of 200m against each other so how long will it take them to reach each other?

$${two}\:{cars}\:{moving}\:{at}\:{speed}\:{of}\:\mathrm{10}\frac{{m}}{{sec}}\:{and}\: \\ $$$$\mathrm{16}\frac{{m}}{{sec}}\:{on}\:{a}\:{road}\:{with}\:{a}\:{length}\:{of}\:\mathrm{200}{m} \\ $$$${against}\:{each}\:{other}\:{so}\:{how}\:{long}\:{will} \\ $$$${it}\:{take}\:{them}\:{to}\:{reach}\:{each}\:{other}? \\ $$

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point A is at the bottom of a rough plane which is inclined at an angle Θ to the horizontal. A body of mass m is projected from A along and end up a line of greatest slope (along the plane). the cofficient of friction between the body and the plane is ϕ. it then comes to rest at point B at a distance X from A. obtain the expression for (a) the workdone against friction when the body moves from A to B and back to A (ii) initial speed of the body (iii) the speed of the body on its return to A

$${point}\:{A}\:{is}\:{at}\:{the}\:{bottom}\:{of}\:{a}\:{rough}\: \\ $$$${plane}\:{which}\:{is}\:{inclined}\:{at}\:{an}\:{angle}\: \\ $$$$\Theta\:{to}\:{the}\:{horizontal}.\:{A}\:{body}\:{of}\:{mass}\: \\ $$$${m}\:{is}\:{projected}\:{from}\:{A}\:{along}\:{and}\:{end}\: \\ $$$${up}\:{a}\:{line}\:{of}\:{greatest}\:{slope}\:\left({along}\:{the}\right. \\ $$$$\left.{plane}\right).\:{the}\:{cofficient}\:{of}\:{friction}\:{between} \\ $$$${the}\:{body}\:{and}\:{the}\:{plane}\:{is}\:\varphi.\:{it}\:{then}\: \\ $$$${comes}\:{to}\:{rest}\:{at}\:{point}\:{B}\:{at}\:{a}\:{distance}\:{X}\: \\ $$$${from}\:{A}.\:{obtain}\:{the}\:{expression}\:{for} \\ $$$$\left({a}\right)\:{the}\:{workdone}\:{against}\:{friction} \\ $$$${when}\:{the}\:{body}\:{moves}\:{from}\:{A}\:{to}\:{B} \\ $$$${and}\:{back}\:{to}\:{A} \\ $$$$\left({ii}\right)\:{initial}\:{speed}\:{of}\:{the}\:{body} \\ $$$$\left({iii}\right)\:{the}\:{speed}\:{of}\:{the}\:{body}\:{on}\:{its}\: \\ $$$${return}\:{to}\:{A} \\ $$

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the speed v of a projectile launched at an angle α to the horizontal is thought to be given by : v = [(1/k)(A + ((sin αt)/g)) + e^(−C/t) ] where k,A, α and C are constants, t is time and g is the gravitational acceleration. determine the base units of A, α and C

$$\mathrm{the}\:\mathrm{speed}\:{v}\:\mathrm{of}\:\mathrm{a}\:\mathrm{projectile}\:\mathrm{launched}\:\mathrm{at} \\ $$$$\mathrm{an}\:\mathrm{angle}\:\alpha\:\mathrm{to}\:\mathrm{the}\:\mathrm{horizontal}\:\mathrm{is}\:\mathrm{thought}\:\mathrm{to} \\ $$$$\mathrm{be}\:\mathrm{given}\:\mathrm{by}\:: \\ $$$$\:\:\:\:\:\:\:{v}\:=\:\left[\frac{\mathrm{1}}{{k}}\left({A}\:+\:\frac{\mathrm{sin}\:\alpha{t}}{\mathrm{g}}\right)\:+\:{e}^{−{C}/{t}} \right] \\ $$$$\mathrm{where}\:{k},{A},\:\:\alpha\:\mathrm{and}\:{C}\:\mathrm{are}\:\mathrm{constants},\:{t}\:\mathrm{is}\:\mathrm{time} \\ $$$$\mathrm{and}\:\mathrm{g}\:\mathrm{is}\:\mathrm{the}\:\mathrm{gravitational}\:\mathrm{acceleration}. \\ $$$$\mathrm{determine}\:\mathrm{the}\:\mathrm{base}\:\mathrm{units}\:\mathrm{of}\:{A},\:\alpha\:\mathrm{and}\:{C} \\ $$

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a man hits a golf ball at the top of a cliff which is 40.0 m high. given that the ball falls into a water down cliff and he hears the sound 3 s after he hit the ball. what is the initial speed of the ball. take the speed of sound in air as 343 m/s. neglect air resistance.

$$\mathrm{a}\:\mathrm{man}\:\mathrm{hits}\:\mathrm{a}\:\mathrm{golf}\:\mathrm{ball}\:\mathrm{at}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{a}\:\mathrm{cliff} \\ $$$$\mathrm{which}\:\mathrm{is}\:\mathrm{40}.\mathrm{0}\:\mathrm{m}\:\mathrm{high}.\:\mathrm{given}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{ball}\:\mathrm{falls}\:\mathrm{into}\:\mathrm{a}\:\mathrm{water}\:\mathrm{down}\:\mathrm{cliff}\:\mathrm{and}\:\mathrm{he} \\ $$$$\mathrm{hears}\:\mathrm{the}\:\mathrm{sound}\:\mathrm{3}\:\mathrm{s}\:\mathrm{after}\:\mathrm{he}\:\mathrm{hit}\:\mathrm{the}\:\mathrm{ball}. \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{initial}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ball}.\:\mathrm{take} \\ $$$$\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{sound}\:\mathrm{in}\:\mathrm{air}\:\mathrm{as}\:\mathrm{343}\:\mathrm{m}/\mathrm{s}.\:\mathrm{neglect} \\ $$$$\mathrm{air}\:\mathrm{resistance}. \\ $$

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A 50g golf ball is struck with a club moving with a velocity of 22m/s after it moves 4cm and ball accelerates with a velocity of 44m/s. estimate the average force exerted by the club on the ball.

$$ \\ $$$$\mathrm{A}\:\mathrm{50g}\:\mathrm{golf}\:\mathrm{ball}\:\mathrm{is}\:\mathrm{struck}\:\mathrm{with}\:\mathrm{a}\:\mathrm{club}\:\mathrm{moving} \\ $$$$\mathrm{with}\:\mathrm{a}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{22m}/\mathrm{s}\:\mathrm{after}\:\mathrm{it}\:\mathrm{moves}\:\mathrm{4cm}\:\mathrm{and} \\ $$$$\mathrm{ball}\:\mathrm{accelerates}\:\mathrm{with}\:\mathrm{a}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{44m}/\mathrm{s}. \\ $$$$\mathrm{estimate}\:\mathrm{the}\:\mathrm{average}\:\mathrm{force}\:\mathrm{exerted}\:\mathrm{by}\:\mathrm{the}\:\mathrm{club} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{ball}. \\ $$

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