A 10 kg weight is attached to a spring with constant k = 90 kg/m and subjected to an external force F(t) = -640 sin(5t). The weight begins at rest in its equilibrium position. Find its displacement for t > 0, with y(t) measured positive upwards. y(t)
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- Am = 4.4 kg block rests on a horizontal surface with coefficient of frictionµ = 0.102. It is attached to a horizontal spring of (stiffness) spring constant k = 12.2 N/m which is anchored to a wall. With the block initially at rest and the spring initially unstretched, a force F,= 30.3 N, 0 = 27.7° above the horizontal is applied to the block (as shown), dragging it 34.0 cm. Www m a) Draw a free-body diagram showing all the forces acting on the block. b) Calculate the net below. (Give your answer to 3 sig. figs.) on the ter your value in blank c) Find the final speed of the block. Your Answer: Answer unitsYou pull on a string with a horizontal force of magnitude Fyb = 69 N that is attached to a block of mass m 6 kg, then to the axle of a solid cylinder of mass me = 4.4 kg and radius r = 0.5 m, then to a spring of spring constant k = 115 N/m. This is all done on an inclined plane where there is friction (μs = 0.65 and μk = 0.36), and the incline angle is 0 = 30 degrees. Everything starts at rest, and the spring is unstretched. The block slides down the plane, the cylinder rolls down the plane (without slipping), and the spring stretches. k lllllllll Fyb b 0 Speed First, what is the speed of the block and cylinder after you have pulled the block and cylinder 172 cm down the plane? V=A spring is attached to a block with a mass of 2.33 kg. The block is set on a rough horizonal surface, and you pull horizontally on the other end of the spring, steadily increasing the force. As soon as the spring stretches 0.126 m beyond its equilibrium length, you notice the block starts to move. If the spring constant is 75.8 N/m, what is the coefficient of static friction between the block and the surface?
- You have a light spring which obeys Hooke's law. This spring stretches 3.28 cm vertically when a 2.70 kg object is suspended from it. Determine the following.A mass m = 0.851 kg cart standing over a horizontal air track is attached to a string as it is shown in the figure. The string passes over a pulley of mass M=1.45 kg and radrus R= 40.4 cm (I=1/2 MR-) and is pulled with a constant force F, as shown in the figure. If the air passing through the track is turned off, wwhat is the magnitude of the constant force F that will accelerate the cart to an acceleration a 3.64 m/s-? The static and kinetic friction between the cart and the air-track are u, = 0.75 and 0.4 respectively (q715) aant a) 09.07 N b) 05.74 N c) O3.44 N d) O8.1 NThree forces act on a statue. Force F⃗ 1F→1 (magnitude 45.0 NN) points in the +x-direction, Force F⃗ 2F→2 (magnitude 105 NN) points in the +y-direction, and force F⃗ 3F→3 (magnitude 235 NN) is at an angle of 36.9∘∘ from the -x-direction and 53.1∘∘ from the +y-direction. counterclockwise from the +x-direction. Find the x- and y-components of the net external force F⃗ F→ on the statue. Find the magnitude and direction of the net external force exerted on the statue.
- A block weighing 14.0 N can slide without friction on an inclined plane at an angle of 40.0 degrees. At one end of the beam is attached a light spring which has a length when not stretched of 0.450 m and a spring constant of 120 N / m. determine the equation of motion of the block by taking the xy coordinates (horizontal x and y vertical)!A bullet with mass 4.95 g is fired horizontally into a 1.972-kg block attached to a horizontal spring. The spring has a constant 5.71 x 102 N/m and reaches a maximum compression of 6.44 cm. (a) Find the initial speed of the bullet-block system. m/s (b) Find the speed of the bullet. m/sA 0.35 kg mass is held against a compressed spring with a spring constant of 89 N/m. The mass is initially at rest upon a horizontal surface and the spring force is directed parallel to the plane of the surface. If the coefficient of kinetic friction is 0.86, with what speed does the mass leave contact with the spring if the spring is initially compressed by 0.232 m?