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MechanicsQuestion and Answers: Page 7

Question Number 153041 Answers: 3 Comments: 0

A ball is thrown vertically upwards with a velocity of 10 ms^(−1) from a point 75m above the ground. How long will it take the ball to strike the ground?

$$\mathrm{A}\:\mathrm{ball}\:\mathrm{is}\:\mathrm{thrown}\:\mathrm{vertically}\:\mathrm{upwards} \\ $$$$\mathrm{with}\:\mathrm{a}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{10}\:{ms}^{−\mathrm{1}} \:\mathrm{from}\:\mathrm{a}\:\mathrm{point} \\ $$$$\mathrm{75}{m}\:\mathrm{above}\:\mathrm{the}\:\mathrm{ground}.\:\mathrm{How}\:\mathrm{long}\:\mathrm{will} \\ $$$$\mathrm{it}\:\mathrm{take}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{to}\:\mathrm{strike}\:\mathrm{the}\:\mathrm{ground}? \\ $$

Question Number 152388 Answers: 1 Comments: 8

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Question Number 147149 Answers: 1 Comments: 0

Two concurrent forces F_1 = 12N and F_2 = 30N are 150° apart. Calculate the angle between F_2 and the resultant force.

$$\:\mathrm{Two}\:\mathrm{concurrent}\:\mathrm{forces}\:\boldsymbol{{F}}_{\mathrm{1}} \:=\:\mathrm{12N}\:\mathrm{and} \\ $$$$\:\boldsymbol{{F}}_{\mathrm{2}} \:=\:\mathrm{30N}\:\mathrm{are}\:\mathrm{150}°\:\mathrm{apart}.\:\mathrm{Calculate}\: \\ $$$$\:\mathrm{the}\:\mathrm{angle}\:\mathrm{between}\:\boldsymbol{{F}}_{\mathrm{2}} \:\mathrm{and}\:\mathrm{the}\:\mathrm{resultant} \\ $$$$\:\mathrm{force}. \\ $$

Question Number 147147 Answers: 0 Comments: 0

One end of an inextensible string is fixed to a ceiling and the other end is tied to a wooden block. The block is pulled aside by a horizontal force P, such that the string now makes an angle of 45° with the downward vertical. When the force P is raised through an angle of 30°, it decreases by 8N to keep the system in equilibrium without shifting the string. Find the (a) value of P. (b) mass of the block.

$$\:\mathrm{One}\:\mathrm{end}\:\mathrm{of}\:\mathrm{an}\:\mathrm{inextensible}\:\mathrm{string}\:\mathrm{is} \\ $$$$\:\mathrm{fixed}\:\mathrm{to}\:\mathrm{a}\:\mathrm{ceiling}\:\mathrm{and}\:\mathrm{the}\:\mathrm{other}\:\mathrm{end}\:\mathrm{is} \\ $$$$\:\mathrm{tied}\:\mathrm{to}\:\mathrm{a}\:\mathrm{wooden}\:\mathrm{block}.\:\mathrm{The}\:\mathrm{block}\:\mathrm{is} \\ $$$$\:\mathrm{pulled}\:\mathrm{aside}\:\mathrm{by}\:\mathrm{a}\:\mathrm{horizontal}\:\mathrm{force}\:\boldsymbol{{P}}, \\ $$$$\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{string}\:\mathrm{now}\:\mathrm{makes}\:\mathrm{an} \\ $$$$\:\mathrm{angle}\:\mathrm{of}\:\mathrm{45}°\:\mathrm{with}\:\mathrm{the}\:\mathrm{downward}\: \\ $$$$\:\mathrm{vertical}.\:\mathrm{When}\:\mathrm{the}\:\mathrm{force}\:\boldsymbol{{P}}\:\:\mathrm{is}\:\mathrm{raised} \\ $$$$\:\mathrm{through}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{30}°,\:\mathrm{it}\:\mathrm{decreases}\:\mathrm{by} \\ $$$$\:\mathrm{8N}\:\mathrm{to}\:\mathrm{keep}\:\mathrm{the}\:\mathrm{system}\:\mathrm{in}\:\mathrm{equilibrium} \\ $$$$\:\mathrm{without}\:\mathrm{shifting}\:\mathrm{the}\:\mathrm{string}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\:\:\:\:\:\:\:\:\:\left({a}\right)\:\mathrm{value}\:\mathrm{of}\:\boldsymbol{{P}}. \\ $$$$\:\:\:\:\:\:\:\:\:\left({b}\right)\:\mathrm{mass}\:\mathrm{of}\:\mathrm{the}\:\mathrm{block}. \\ $$

Question Number 146303 Answers: 2 Comments: 4