2. A particle moves in a medium under the influence of a retarding force equal to mk(v + a?v), where k and a are constants. Show that for any value of the initial speed the particle will never move a distance greater than /2ka and that the particle comes to rest only for t → ∞.
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- A man does 4,730 J of work in the process of pushing his 2.30 × 10³ kg truck from rest to a speed of v, over a distance of 26.0 m. Neglecting friction between truck and road, determine the following. (a) the speed v (in m/s) m/s (b) the horizontal force exerted on the truck (in N) N6. A small block slides down a frictionless track whose shape is described by y = (x^2) /d for x<0 and by y = -(x^2)/d for x>0. The value of d is 4.68 m, and x and y are measured in meters as usual. Suppose the block starts from rest on the track, at x = -1.17 m. What will the block s speed be when it reaches x = 0? 1.70 m/s 1.19 m/s 3.12 m/s 2.40 m/sTwo objects are connected by a light string passing over a light, frictionless pulley. The 5.00-kg object is released from rest at a point 4.00 m above the floor. Find the speed of the 5.00-kg object when it is 1 meter above the floor. m, = 5.00 kg h = 4.00 m m, = 3.00 kg 4.756 m/s 3.834 m/s 4.475 m/s 3.942 m/s 4.135 m/s 3.384 m/s А. D. В. Е. С. F.
- A 5.8 × 105 kg train is brought to a stop from a speed of 0.85 m/s in 0.57 m by a large spring bumper at the edge of its track. What is the force constant k of the spring in N/m?= A large spring with spring constant k 550 N/m is oriented vertically on a table. When the spring is at its relaxed length, a book with mass m = 1.3 kg is gently placed on top and released from rest. Through what vertical distance d has the book dropped when the spring reaches its maximum compression? What is the book's speed when it is halfway between its release position and its lowest position?A 0.25 kg mass is placed on a vertically oriented spring that is stretched 0.56 meters from its equilibrium position. If the spring constant is 105 N/m, how fast will the mass be moving when it reaches the equilibrium position? Hint: You cannot ignore the change in gravitational potential energy in this problem. Please give you’re answer in m/s.
- Object b has a mass mb and starts from rest at position x=xi, where xi>0. Derive an expression for the speed of the particle when it is at the position x=xf.A 6.00 ✕ 105 kg subway train is brought to a stop from a speed of 0.500 m/s in 0.400 m by a large spring bumper at the end of its track. What is the force constant k of the spring?2. Tarzan, whose weight is W = 688 N, swings from a vine of length L = 18 m. He starts his swing from rest at the edge of a cliff that is h = 3.2 m above the bottom of his trajectory. The vine will break if its tension exceeds T 900 N. W (a) Does the vine break? If the vine does not break, what is the greatest (b) tension in the vine? If the vine breaks, at what angle with respect to the vertical will it break?
- 29.A particle of mass 2.0 kg moves under the influence of the force F(x)=(−5x² +7x) N. If its speed at x=-4.0 m is v=20.0 m/s, what is its speed at x = 4.0 m? Solution 14 m/s3. A 60 kg snowboarder begins to slide down the hill 50 m high on a smooth surface with a radius curvature of 80 m. The next section (AB) is a 20 m flat rough track with u = .3, at the end of which there is an elastic barrier with k = 1000 N/m. Find her speed at point A. b. How much work is done by frictional force? c. What is the maximum compression of the spring? d. Find the rate of heat dissipation along the section AB. e. How long does it take to cover the section AB? а. h k ВQUESTION 8 OK, same sort of track, but now with d = 2.10 m. Now suppose the blocks starts on the track at x = 4.76 m. The block is given a push to the left and begins to slide up the track, eventually reaching its maximum height at x = 0, at which point it turns around and begins sliding down. What was its initial speed in this case? A 8.30 m/s B 14.55 m/s C 10.29 m/s D 17.39 m/s