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Calculate the power output needed for a 950-kg car to climb a $2.00\text{\xb0}$ slope at a constant 30.0 m/s while encountering wind resistance and friction totaling 600 N.
A man of mass 80 kg runs up a flight of stairs 20 m high in 10 s. (a) how much power is used to lift the man? (b) If the man’s body is 25% efficient, how much power does he expend?
a. 1.57 kW; b. 6.28 kW
The man of the preceding problem consumes approximately $1.05\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{7}\phantom{\rule{0.2em}{0ex}}\text{J}$ (2500 food calories) of energy per day in maintaining a constant weight. What is the average power he produces over a day? Compare this with his power production when he runs up the stairs.
An electron in a television tube is accelerated uniformly from rest to a speed of $8.4\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{7}\phantom{\rule{0.2em}{0ex}}\text{m/s}$ over a distance of 2.5 cm. What is the power delivered to the electron at the instant that its displacement is 1.0 cm?
$6.83\text{\mu W}$
Coal is lifted out of a mine a vertical distance of 50 m by an engine that supplies 500 W to a conveyer belt. How much coal per minute can be brought to the surface? Ignore the effects of friction.
A girl pulls her 15-kg wagon along a flat sidewalk by applying a 10-N force at $37\text{\xb0}$ to the horizontal. Assume that friction is negligible and that the wagon starts from rest. (a) How much work does the girl do on the wagon in the first 2.0 s. (b) How much instantaneous power does she exert at $t=2.0\phantom{\rule{0.2em}{0ex}}\text{s}$ ?
a. 8.51 J; b. 8.51 W
A typical automobile engine has an efficiency of 25%. Suppose that the engine of a 1000-kg automobile has a maximum power output of 140 hp. What is the maximum grade that the automobile can climb at 50 km/h if the frictional retarding force on it is 300 N?
When jogging at 13 km/h on a level surface, a 70-kg man uses energy at a rate of approximately 850 W. Using the facts that the “human engine” is approximately 25% efficient, determine the rate at which this man uses energy when jogging up a $5.0\text{\xb0}$ slope at this same speed. Assume that the frictional retarding force is the same in both cases.
1.7 kW
A cart is pulled a distance D on a flat, horizontal surface by a constant force F that acts at an angle $\theta $ with the horizontal direction. The other forces on the object during this time are gravity ( ${F}_{w}$ ), normal forces ( ${F}_{N1}$ ) and ( ${F}_{N2}$ ), and rolling frictions ${F}_{r1}$ and ${F}_{r2}$ , as shown below. What is the work done by each force?
Consider a particle on which several forces act, one of which is known to be constant in time: ${\overrightarrow{F}}_{1}=(3\phantom{\rule{0.2em}{0ex}}\text{N})\widehat{i}+(4\phantom{\rule{0.2em}{0ex}}\text{N})\widehat{j}.$ As a result, the particle moves along the x -axis from $x=0$ to $x=5\phantom{\rule{0.2em}{0ex}}\text{m}$ in some time interval. What is the work done by ${\overrightarrow{F}}_{1}$ ?
$15\phantom{\rule{0.2em}{0ex}}\text{N}\xb7\text{m}$
Consider a particle on which several forces act, one of which is known to be constant in time: ${\overrightarrow{F}}_{1}=(3\phantom{\rule{0.2em}{0ex}}\text{N})\widehat{i}+(4\phantom{\rule{0.2em}{0ex}}\text{N})\widehat{j}.$ As a result, the particle moves first along the x -axis from $x=0$ to $x=5\phantom{\rule{0.2em}{0ex}}\text{m}$ and then parallel to the y -axis from $y=0$ to $y=6\phantom{\rule{0.2em}{0ex}}\text{m}\text{.}$ What is the work done by ${\overrightarrow{F}}_{1}$ ?
Consider a particle on which several forces act, one of which is known to be constant in time: ${\overrightarrow{F}}_{1}=(3\phantom{\rule{0.2em}{0ex}}\text{N})\widehat{i}+(4\phantom{\rule{0.2em}{0ex}}\text{N})\widehat{j}.$ As a result, the particle moves along a straight path from a Cartesian coordinate of (0 m, 0 m) to (5 m, 6 m). What is the work done by ${\overrightarrow{F}}_{1}$ ?
$39\phantom{\rule{0.2em}{0ex}}\text{N}\xb7\text{m}$
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