The displacement of a block attached to a horizontal spring whose spring constant is 14N/m is given by x = 0.7m x cos (2,8 t - 0.8). kg. The block is of mass 1.78 J. The total energy of the system is 3.43 What is the earliest time (t > 0) when the kinetic energy equals one-half the potential energy? m/s². The acceleration of the block at t = 0.3 s is S.
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- An ideal spring hangs from the ceiling. A 1.75 kg mass is hung from the spring, stretching the spring a distance d=0.0865 m from its original length when it reaches equilibrium. The mass is then lifted up a distance L=0.0295 m from the equilibrium position and released. What is the kinetic energy of the mass at the instant it passes back through the equilibrium position?A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 8 inches below the equilibrium position. (a) Find the position x of the mass at the times t = n/12, n/8, n/6, a/4, and 97/32 s. (Use g = 32 ft/s? for the acceleration due to gravity.) X(1/12) = -0.33 X ft x(x/8) = -0.66 X ft x(л/6) %3 -0.33 X ft x(T/4) = 0.66 X ft x(9x/32) = 0.47 X ft (b) What is the velocity of the mass when t = 37/16 s? 16 ft/s 3 In which direction is the mass heading at this instant? upward downward (c) At what times does the mass pass through the equilibrium position? 16 4 X , n = 0, 1, 2, +2. A 10.0-kg block is released from rest at a rough 5.0 m long 30° incline. The coefficient of kinetic friction between incline and box is 0.2. At the bottom of the incline is a frictionless flat track. The block travels down the track, hits a spring of force constant k = 100 N/m. Determine (a) the speed of the block at the bottom of the incline, (b) the maximum compressing distance of the spring from its equilibrium position. (25) 30° spring
- Pls help ASAP.A horizontal block-spring system with the block on a frictionless surface has total mechanical energy E = 46.9 J and a maximum displacement from equilibrium of 0.227 m. (a) What is the spring constant? 1820.3 N/m (b) What is the kinetic energy of the system at the equilibrium point? 46.9 J (c) If the maximum speed of the block is 3.45 m/s, what is its mass? 7.88 kg (d) What is the speed of the block when its displacement is 0.160 m? m/s (e) Find the kinetic energy of the block at x = 0.160 m. J (f) Find the potential energy stored in the spring when x = 0.160 m. J (g) Suppose the same system is released from rest at x = 0.227 m on a rough surface so that it loses 12.1 J by the time it reaches its first turning point (after passing equilibrium at x = 0). What is its position at that instant? mAn automobile having a mass of 1000 kg is driven into a brick wall in a safety test. The bumper behaves like a spring with constant 4.75 106 N/m and is compressed 2.70 cm as the car is brought to rest. What was the speed of the car before impact, assuming no energy is lost in the collision with the wall? m/s
- A block of mass m = 2.00 kg is attached to a spring of force constant k = 550 N/m as shown in the figure below. The block 4.60 cm to the right of equilibrium and released from rest. is pulled to a position x; = x = 0 m (a) Find the speed the block has as it passes through equilibrium if the horizontal surface is frictionless. 0.73 How much energy is stored in the spring when it is at equilibrium? m/s Need Help? x = x₂ (b) Find the speed the block has as it passes through equilibrium (for the first time) if the coefficient of friction between block and surface is = 0.350. інк 0.500 X The force of friction causes an increase in the internal energy of the system and a decrease in the total mechanical energy. m/s Read It Watch ItHelp thank you! An object is attached to an ideal spring of spring constant 2.61 N/m. The spring is initially in its relaxed position. The object is then released and oscillates about its equilibrium position. The motion is described by y= (5.55 cm) sin [(0.700 rad/s)f]. What is the maximum kinetic energy?wwww wwww A block with mass m = 5 kg is attached to two springs with spring constants kleft = 31 N/m and kright = 56 N/m. The block is pulled a distance x = 0.23 m to the left of its equilibrium position and released from rest.
- 4. A spring with an equilibrium length of 50.0 cm is holding a 4.00kg mass. The mass causes the spring to stretch to a length of 1.00 meter. What is the potential energy given to the spring?hass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 9 inches below the equilibrium position. (a) Find the position x of the mass at the timest= 1/12, 1/8, 1/6, 11/4, and 91/32 s. (Use g = 32 ft/s? for the acceleration due to gravity.) x(n/12) = ft x(n/8) = ft x(п/6) — ft x(п/4) — ft x(9n/32) ft (b) What is the velocity of the mass when t = 3t/16 s? ft/s In which direction is the mass heading at this instant? O downward O upward (c) At what times does the mass pass through the equilibrium position? п 3D 0, 1, 2, ..9. A 7.9 kg object is suspended 10 m above the ground. Directly beneath it is a spring with a spring constant of 6500 N/m. Qualitatively describe what occurs to the energy of the system once the object is released? (Hint: Consider what occurs as the object falls, encounters the spring, and if it will go back up again!)