An ideal spring with k = 8 N/m is initially compressed 0.40 m. One end is attached to a wall and the other is attached to a 1.0 kg block. The block is released from rest and slides 0.20 m on the horizontal surface before coming to rest (the spring is still compressed by 0.20 m at this time). The coefficient of kinetic friction between the block and surface is Funk M X=0
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- of k = 700 N/m. A block of mass m = 1.10 kg is attached to the spring and rests on a frictionless, horizontal surface as in the figure below. The left end of a horizontal spring is attached to a vertical wall, and the right end is attached to a block of mass m. The spring has force constant k. Three positions are labeled along the spring, and the block is pulled to the rightmost position, stretching the spring. The leftmost position, the equilibrium position, is labeled x = 0. The middle position, halfway between the leftmost and rightmost positions, is labeled x = xi⁄2. The rightmost position is labeled x = xi. (a) The block is pulled to a position xi = 6.80 cm from equilibrium and released. Find the potential energy stored in the spring when the block is 6.80 cm from equilibrium. J(b) Find the speed of the block as it passes through the equilibrium position. m/s(c) What is the speed of the block when it is at a position xi/2 = 3.40 cm? m/sYou push a 2.00 kg block against a horizontal spring, compressing the spring by 15.0 cm. Then you release the block, and the spring sends it sliding across a frictionless tabletop for 30.0 cm. The block then moves up an 30.0°-incline plane and it moves up the incline for 65.0 cm before coming to rest. If the spring constant is 1000.0 N/m, determine the coefficient of kinetic friction between the block and the incline plane.A block of mass 11.0 kg slides from rest down a frictionless 36.0° incline and is stopped by a strong spring with k = 2.30 ✕ 104 N/m. The block slides 3.00 m from the point of release to the point where it comes to rest against the spring. When the block comes to rest, how far has the spring been compressed?
- A 0.28 kg mass is held against a compressed spring with a spring constant of 2,446 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 0.716, with what speed does the mass leave contact with the spring if the spring is initially compressed by 0.068 m?The elastic energy stored in your tendons can contribute up to 35% of your energy needs when running. Sports scientists have studied the change in length of the knee extensor tendon in sprinters and nonathletes. They find (on average) that the sprinters’ tendons stretch 41 mm, while nonathletes’ stretch only 33 mm. The spring constant for the tendon is the same for both groups, 33 N/mm. What is the difference in maximum stored energy between the sprinters and the nonathletes?A block of mass 2.9 kg is sitting on a frictionless ramp with a spring at the bottom that has a spring constant of 470 N/m (refer to the figure). The angle of the ramp with respect to the horizontal is 13°. a) The block, starting from rest, slides down the ramp a distance 54 cm before hitting the spring. How far, in centimeters, is the spring compressed as the block comes to momentary rest? b) After the block comes to rest, the spring pushes the block back up the ramp. How fast, in meters per second, is the block moving right after it comes off the spring? c) What is the change of the gravitational potential energy, in joules, between the original position of the block at the top of the ramp and the position of the block when the spring is fully compressed?
- A glider of mass 0.240 kg is on a horizontal track, attached to a horizontal spring of force constant 6.00 N/m. There is friction between the track and the glider. Initially the spring (whose other end is fixed) is stretched by 0.100 m and the attached glider is moving at 0.400 m>s in the direction that causes the spring to stretch farther. The glider comes momentarily to rest when the spring is stretched by 0.112 m. (a) How much work does the force of friction do on the glider as the stretch of the spring increases from 0.100 m to 0.112 m? (b) What is the coefficient of kinetic friction between the glider and the track?A block of mass 15.0 kg slides from rest down a frictionless 33.0° incline and is stopped by a strong spring with k = 4.00 ✕ 104 N/m. The block slides 3.00 m from the point of release to the point where it comes to rest against the spring. When the block comes to rest, how far has the spring been compressed?10. A block with mass 0.50 kg is forced against a horizontal spring of negligible mass, compressing the spring a distance of 0.20 m (Fig. P43). When released, the block moves on a horizontal table top for 1.00 m before coming to rest. The spring constant k is 100 N/m. What is the coefficient of kinetic friction between the block and the table top? Figure P43 k- 100 Nim -0.50 kg 1.00 m-
- A 1.50-kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Figure a). The object has a speed of v. = 2.80 m/s when it makes contact with a light spring (Figure b) that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distance d (Figure c). The object is then forced toward the left by the spring (Figure d) and continues to move in that direction beyond the spring's unstretched position. Finally, the object comes to rest a distance D to the left of the unstretched spring (Figure e). a m Vj = V=0 k (a) Find the distance of compression d (in m). m (b) Find the speed v (in m/s) at the unstretched position when the object is moving to the left (Figure d). m/s (c) Find the distance D (in m) where the object comes to rest. m (d) What If? If the object becomes attached securely to the end of the spring when it makes contact, what is the new value of the distance D (in m) at which the object will come to rest…To measure the static friction coefficient between a 1.40-kg block and a vertical wall, a spring (k = 770 N/m) is attached to the block, is pushed on the end in a direction perpendicular to the wall until the block does not slip downward (see figure). If the spring is compressed by 0.048 m, what is the coefficient of static friction?An ideal spring is attached to the ceiling. While the spring is held at its relaxed length, a wooden block (M = 850 g) is attached to the bottom of the spring, and a ball of clay (m = 210 g) is pressed onto the bottom of the block so that they stick together. The block+clay are gently lowered through a distance of d = 2.7 cm and are then released, at which point they hang motionlessly from the bottom of the spring. After a few minutes have passed, the clay unsticks itself from the block and falls from rest to the ground. 1. What is the resulting period T of the block’s oscillation after the separation occurs? 2. As d approaches 0, what limit does T approach?