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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
Physics for Scientists and Engineers, Technology Update (No access codes included)
- 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_forwardIn the figure, a force P acts on a block weighing 45.0 N. The block is initially at rest on a plane inclined at angle = 18.0° to the horizontal. The positive direction of the x axis is up the plane. The coefficients of friction between block and plane are μ = 0.540 and Uk = 0.340. In unit-vector notation, what is the frictional force on the block from the plane when Pis (a) (-5.30 N)î, (b) (-8.10 N)î, and (c) (-15.1 N)? (a) Number i (b) Number i (c) Number i i+ i+ i i i+ i j Units j Units j Unitsarrow_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_forward
- Particles 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_forwardDetermine the force Q-> when the block moves with constant velocity. Express your answer in vector form.arrow_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_forward
- A block of mass m =1 kg, slides down a rough incline with constant velocity. The coefficient of kinetic friction between the block and the incline is µr, and the incline makes an angle 0 = 30° horizontal. Take g = 10 m/s2. The coefficient of kinetic friction µ is then equal to: v= constant with the O 0.577 O 0.466 O 0.422 O 0.364arrow_forwardA cart of mass 8.00 kg was moved by applying two constant forces. Force 1 is 28.0 N at 42.0°, and Force 2 is 13.0 N at 110°. Initially, the cart has a velocity of (3.50 i +2.20 j) m/s. a. Express the two forces in in unit-vector notation. Ans. F = (20.81 i+ 18.74 j)N, F, =(-4.45 i+ 12.22 j)N b. Find the total force exerted on the cart. Ans. EF = (16.36 i + 30.96 j)N or 35.02 N c. Find the angle at which the total force is applied. Ans. 62.15º d. What is the acceleration of the cart? Ans. å = (2.05 i + 3.87 j)" or 4.38 EERINarrow_forwardA cart of mass 8.00 kg was moved by applying two constant forces. Force 1 is 28.0 N at 42.0°, and Force 2 is 13.0 N at 110°. Initially, the cart has a velocity of (3.50 i +2.20 j) m/s. a. Express the two forces in in unit-vector notation. Ans. F = (20.81 i + 18.74 j)N, F, = (-4.45 i + 12.22 j)N b. Find the total force exerted on the cart. Ans. EF = (16.36 i + 30.96 j)N or 35.02 N Find the angle at which the total force is applied. Ans. 62.15° NEERINarrow_forward
- A large crate with mass mm rests on a horizontal floor. The static and kinetic coefficients of friction between the crate and the floor are μsμs and μkμk, respectively. A woman pushes downward on the crate at an angle θθ below the horizontal with a force F⃗ F→. 1. What is the magnitude of the force vector F⃗ F→ required to keep the crate moving at constant velocity? Express your answer in terms of mmm, ggg, θθ, and μkμk.arrow_forwardA 20-kg particle moves with this trajectory: r ( t ) = − 40 t ȷ ^ + 25 t ı ^ + ( 5 ı ^ − 8 ȷ ^ ) e − 5 t Calculate the force on the particle. (Units are meters, seconds, and Newtons.)arrow_forwardA stacked pair of books with masses m1= 2.0 kg (bottom book) and m2 = 1.5 kg (top book) are tossed onto a table. The books strike the table with no vertical velocity and their common horizontal speed is ?o = 0.75 m/s. The kinetic friction coefficient between the bottom book and the table is ?k1=0.45; the kinetic and static friction coefficients between the two books are ?k2=0.3 and ?s2= 0.4. Find the final horizontal position of each book relative to the spot where the stack hits the table.arrow_forward
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