Problem 5.62

a) จาก \(m = 500 kg, \vec{u} = 0 m/s, \vec{v} = 2.00 m/s\) และ \(Δt = 3.00 s\)

พิจารณา F.B.D.

T

จาก \(Σ\vec{F} = m\vec{a}\)

\(T - mg = ma\)

\(T = m(g + a) \cdots \cdots (1)\)

a

\(500g\)

จาก \(\wp =\frac{\Delta W}{\Delta t}\)

\(\wp =\frac{T\Delta y}{\Delta t}; \Delta W = F\Delta r = T\Delta y\)

\(\wp =\frac{m(g + a)\Delta y}{\Delta t}; (1)\)

\(\wp =\frac{m}{\Delta t}(g+v^{2}-u^{2})\Delta y; v^{2} = u^{2} + 2a\Delta y\)

\(2\Delta y\)

\(\wp =\frac{m}{\Delta t}(g\Delta y+v^{2}); u = 0 m/s\)

\(\wp =\frac{m}{\Delta t}(g(\frac{2}{(\vec{v}+\vec{u})\Delta t2}+\frac{v^{2}}{2});\Delta y =\frac{(\vec{v} + \vec{u})\Delta t}{2}\)

\(\wp =\frac{m}{2}(gv+v^{2}); u = 0 m/s\)

\(\wp _{hp}=\frac{m}{2}(gv+\frac{\Delta t}{\Delta tv^{2}})(1hp); 1 hp = 746 W\)

\(746 W\)

\(\wp _{hp}= 7.02 hp \;\blacksquare\)

b) จาก \(m = 500 kg, \vec{v} = 2.00 m/s\) และ \(\vec{a} = 0 m/s^{2}\)

พิจารณา F.B.D. จาก \(Σ\vec{F} = m\vec{a}\)

\(T - mg = m(0)\)

T

\(T = mg \cdots \cdots (2)\)

จาก \(\wp = \vec{F}\cdot \vec{v}\)

\(\wp = Tv\)

\(\wp _{hp}= mgv(\frac{1 hp}{746 W}); (2)\)

\(500g\)

\(\wp _{hp}= 13.1 hp \;\blacksquare\)