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A 75.0-kg woman stands on a bathroom scale in an elevator that accelerates from rest to 30.0 m/s in 2.00 s. (a) Calculate the scale reading in newtons and compare it with her weight. (The scale exerts an upward force on her equal to its reading.) (b) What is unreasonable about the result? (c) Which premise is unreasonable, or which premises are inconsistent?
a. 1860 N, 2.53; b. The value (1860 N) is more force than you expect to experience on an elevator. The force of 1860 N is 418 pounds, compared to the force on a typical elevator of 904 N (which is about 203 pounds); this is calculated for a speed from 0 to 10 miles per hour, which is about 4.5 m/s, in 2.00 s). c. The acceleration $a=1.53\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}g$ is much higher than any standard elevator. The final speed is too large (30.0 m/s is VERY fast)! The time of 2.00 s is not unreasonable for an elevator.
(a) Calculate the minimum coefficient of friction needed for a car to negotiate an unbanked 50.0 m radius curve at 30.0 m/s. (b) What is unreasonable about the result? (c) Which premises are unreasonable or inconsistent?
As shown below, if $M=5.50\phantom{\rule{0.2em}{0ex}}\text{kg,}$ what is the tension in string 1?
189 N
As shown below, if $F=60.0\phantom{\rule{0.2em}{0ex}}\text{N}$ and $M=4.00\phantom{\rule{0.2em}{0ex}}\text{kg,}$ what is the magnitude of the acceleration of the suspended object? All surfaces are frictionless.
As shown below, if $M=6.0\phantom{\rule{0.2em}{0ex}}\text{kg,}$ what is the tension in the connecting string? The pulley and all surfaces are frictionless.
15 N
A small space probe is released from a spaceship. The space probe has mass 20.0 kg and contains 90.0 kg of fuel. It starts from rest in deep space, from the origin of a coordinate system based on the spaceship, and burns fuel at the rate of 3.00 kg/s. The engine provides a constant thrust of 120.0 N. (a) Write an expression for the mass of the space probe as a function of time, between 0 and 30 seconds, assuming that the engine ignites fuel beginning at $t=0.$ (b) What is the velocity after 15.0 s? (c) What is the position of the space probe after 15.0 s, with initial position at the origin? (d) Write an expression for the position as a function of time, for $t>30.0\phantom{\rule{0.2em}{0ex}}\text{s}\text{.}$
A half-full recycling bin has mass 3.0 kg and is pushed up a $40.0\text{\xb0}$ incline with constant speed under the action of a 26-N force acting up and parallel to the incline. The incline has friction. What magnitude force must act up and parallel to the incline for the bin to move down the incline at constant velocity?
12 N
A child has mass 6.0 kg and slides down a $35\text{\xb0}$ incline with constant speed under the action of a 34-N force acting up and parallel to the incline. What is the coefficient of kinetic friction between the child and the surface of the incline?
The two barges shown here are coupled by a cable of negligible mass. The mass of the front barge is $2.00\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{kg}$ and the mass of the rear barge is $3.00\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{kg}\text{.}$ A tugboat pulls the front barge with a horizontal force of magnitude $20.0\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{N,}$ and the frictional forces of the water on the front and rear barges are $8.00\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{N}$ and $10.0\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{N,}$ respectively. Find the horizontal acceleration of the barges and the tension in the connecting cable.
${a}_{x}=0.40\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2}$ and $T=11.2\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{N}$
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