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A seaplane of total mass m lands on a lake with initial speed
(a) Carry nut the integration to determine the speed of the seaplane as a function of time. (b) Sketch a graph of the speed as a function of time. (c) Does the seaplane come to a complete stop after a finite interval of time? (d) Does the seaplane travel a finite distance in stopping?
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Chapter 6 Solutions
Bundle: Physics for Scientists and Engineers, Technology Update, 9th Loose-leaf Version + WebAssign Printed Access Card, Multi-Term
- You drop an object of mass m from a tall building. Suppose the only forces affecting its motion are gravity, and air resistance proportional to the object's speed with positive constant of proportionality k. Let g denote gravitational acceleration (a positive constant). Express the total force in terms of m, g, and the object's velocity v, where upward displacement is considered positive. F = mg - kv Newton's second law tells us that force is equal to mass x acceleration, F = ma. Relating acceleration to velocity, rewrite the equation for total force above as a first order differential equation for v as a function of t. Denote v' as dv dt v(t) m(- dr) this is not an equation. Solve this differential equation for v(t) with the initial condition v(0) = V0. = mg (1-e ==) m k Find the terminal Terminal velocity = mg k X velocity. X syntax error: X Xarrow_forwardThe highest spot on Earth is Mt. Everest, which is 8850 m above sea level. If the radius of the Earth (to sea level) is 6370 km, how much does the magnitude of g change between sea level and the top of Mt. Everest? (G = 6.67 × 10-11 N m2/kg2, and the mass of the Earth is 5.98 × 1024 kg.)arrow_forwardAn electron is a subatomic particle (m = 9.11 x 1031 kg) that is subject to electric forces. An electron moving in the +x direction accelerates from an initial velocity of +5.72 x 105 m/s to a final velocity of 2.64 x 106 m/s while traveling a distance of 0.0783 m. The electron's acceleration is due to two electric forces parallel to the x axis: F1 = 9.44 x 10-17 N, and F2, which points in the -x direction. Find the magnitudes of (a) the net force acting on the electron and (b) the electric force F2. F F FF Voarrow_forward
- An electron is a subatomic particle (m = 9.11 x 10-31 kg) that is subject to electric forces. An electron moving in the +x direction accelerates from an initial velocity of +7.67 x 105 m/s to a final velocity of 2.57 x 106 m/s while traveling a distance of 0.0857 m. The electron's acceleration is due to two electric forces parallel to the x axis: = 7.62 x 10-17 N, and , which points in the -x direction. Find the magnitudes of (a) the net force acting on the electron and (b) the electric force .arrow_forwardParticles 1 and 2 of equal mass are thrown vertically upwards at the same initial velocity vo in a constant gravitational field. Particle 1 is under a negligible air resistance fr = 0 while Particle 2 experiences a resistance of the form fr = mav, where m is the particle's mass, a is a positive constant, and v is the particle's velocity at any point in time. Show that the ratio (t2/t1) of the times required for the particles to reach maximum height is given by t2 avo = 1- + O t1 2g 2g where O denotes higher order terms. In the limit a → 0, your result for t2 must approach t1.arrow_forwardA copper block with mass m = 200 g, is at rest on a glass surface, where the plane makes an angle θθ = 45∘. Assume that the glass surface is frictionless. Calculate the acceleration of the copper block when it is released from rest. Express your result in m/s2. Using the information presented calculate the force acting on the mass, m = 200 g, just as it is released from the top of the inclined plane, at y = 8.48 m. Express your answer in Newtons.arrow_forward
- An electron is a subatomic particle (m= 9.11 x 10-31 kg) that is subject to electric forces. An electron moving in the +x direction accelerates from an initial velocity of +7.31 x 105 m/s to a final velocity of 1.98 x 106 m/s while traveling a distance of 0.0545 m. The electron's acceleration is due to two electric forces parallel to the x axis: F₁ = 7.52 x 10-¹7 N, and F2, which points in the -x direction. Find the magnitudes of (a) the net force acting on the electron and (b) the electric force F2. F₁ F₁ F₂ F₁ (a) Number i (b) Number i VO X Units Unitsarrow_forwardAn object with mass m is dropped from rest and we assume that the air resistance is proportional to the speed of the object. If s(t) is the distance dropped after t seconds, then the speed is v = s'(t) and the acceleration is a = v'(t). If g is the acceleration due to gravity, then the downward force on the object is mg − cv, where c is a positive constant, and Newton's Second Law gives m dv dt = mg − cv. (a) Solve this as a linear equation. (Use v for v(t).) v=mgC(1−e−(Cm)t) (b) What is the limiting velocity? lim t → ∞ v(t) = mgc (c) Find the distance the object has fallen after t seconds. (Use s for s(t).)arrow_forwardlo, a satellite of Jupiter, is the most volcanically active moon or planet in the solar system. It has volcanoes that send plumes of matter over 500 km high. Due to the satellite's small mass, the acceleration due to gravity on lo is only 1.81 m/s², and lo has no appreciable atmosphere. Assume that there is no variation in gravity over the distance traveled ▼ What must be the speed of material just as it leaves the volcano altitude of 310 km? Express your answer in meters per second. V = Submit Part B 1ΫΠ| ΑΣΦ U = Request Answer [5] ΑΣΦ Submit ? If the gravitational potential energy is zero at the surface, what is the potential energy for a 35 kg fragment at its maximum height (500 km) on lo? Express your answer in joules. Request Answer m/s ? Constant J reach anarrow_forward
- An electron is a subatomic particle (m accelerates from an initial velocity of +7.54 x 105 m/s to a final velocity of 2.22 x 106 m/s while traveling a distance of 0.0692 m. = 9.11 x 1031 kg) that is subject to electric forces. An electron moving in the +x direction The electron's acceleration is due to two electric forces parallel to the axis: F1 9.04 x 10-17 N, and F2, which points in the -x direction. Find the magnitudes of (a) the net force acting on the electron and (b) the electric force F2 F, F2 F, on with available attempts. (a) Number Units (b) Number Unitsarrow_forwardA piano has been pushed to the top of the ramp at the back of a moving van. The workers think it is safe, but as they walk away, it begins to roll down the ramp. Neglect the friction between the piano and the ramp. If the back of the truck is 1.5 mm above the ground and the ramp is inclined at 26 ∘∘ , how much time do the workers have to get to the piano before it reaches the bottom of the ramp?arrow_forwardParticles q1 = +8.0 x 10^-6, q2 = 3.5 x 10^-6, q3 -2.5 x 10^-6 are in a line. Particles q1 and q2 are separated by 0.10 m and particles q2 and q3 are separated by 0.15 m. What is the net force on particle q1?arrow_forward
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