A lightweight spring with spring constant k = 225 N/m is attached to a block of mass m1 = 4.50 kg on a frictionless, horizontal table. The blockspring system is initially in the equilibrium configuration. A second block of mass m2 = 3.00 kg is then pushed against the first block, compressing the spring by x = 15.0 cm as in Figure P16.77A. When the force on the second block is removed, the spring pushes both blocks to the right. The block m2 loses contact with the springblock 1 system when the blocks reach the equilibrium configuration of the spring (Fig. P16.77B). a. What is the subsequent speed of block 2? b. Compare the speed of block 1 when it again passes through the equilibrium position with the speed of block 2 found in part (a). 77. (a) The energy of the system initially is entirely potential energy. E0=U0=12kymax2=12(225N/m)(0.150m)2=2.53J At the equilibrium position, the total energy is the total kinetic energy of both blocks: 12(m1+m2)v2=12(4.50kg+3.00kg)v2=(3.75kg)v2=2.53J Therefore, the speed of each block is v=2.53J3.75kg=0.822m/s (b) Once the second block loses contact, the first block is moving at the speed found in part (a) at the equilibrium position. The energy 01 this spring-block 1 system is conserved, so when it returns to the equilibrium position, it will be traveling at the same speed in the opposite direction, or v=0.822m/s. FIGURE P16.77

Use the data in Table P16.59 for a block of mass m = 0.250 kg and assume friction is negligible. a. Write an expression for the force FH exerted by the spring on the block. b. Sketch FH versus t.

A spring 1.50 m long with force constant 475 N/m is hung from the ceiling of an elevator, and a block of mass 10.0 kg is attached to the bottom of the spring. (a) By how much is the spring stretched when the block is slowly lowered to its equilibrium point? (b) If the elevator subsequently accelerates upward at 2.00 m/s2, what is the position of the block, taking the equilibrium position found in part (a) as y = 0 and upwards as the positive y-direction. (c) If the elevator cable snaps during the acceleration, describe the subsequent motion of the block relative to the freely falling elevator. What is the amplitude of its motion?

A 0.500 kg mass is hung from a vertical spring which then stretches by 10.5 cm. (a) What is the spring constant? (b) What is the elongation of the spring if the 0.500 kg mass is replaced by a1.25 kg mass?

The springs of a pickup truck act like a single spring with a force constant of k = 1.15 × 105 N/m Part (a)  How many centimeters will the truck be lowered by its maximum load of 920 kg? Part (b)  If the pickup truck has four identical springs, what is the force constant of each, in newtons per meter? Assume the allowed compression is the same as in part (a).

A light elastic string, of natural length 0.8 m and modulus of elasticity 35-4 N, has one end A attached to a fixed point and the other end B attached to a particle P of mass 3 kg. Initially P is held at rest at A. It is then released and allowed to fall. Calculate the speed of P when the length of the string is 1-2 m.

An object is attached to a vertical spring and slowly lowered to its equilibrium position. This stretches the spring by an amount d. If the same object is attached to the same vertical spring but permitted to fall instead, through what maximum distance does it stretch the spring?

A spring AB of natural length 0.5 m and modulus of elasticity 25 N is fixed at A. The other end is joined to another spring BC of natural length 0.8 m and modulus of elasticity 40 N. A weight WN is attached at C and the system hangs vertically in equilibrium so that AC=2m. (i) Find the extension of the two springs. (ii) Find W. Answer: (i) (ii) 0.35 m, 0.35m 17.5 N

A cart of mass 0.72 kg is attached to one end of of a spring and placed on a low-friction track, inclined at an angle of 56.0 degrees with respect to the horizontal. The cart is found to be in equilibrium when the spring is stretched to a total length of 44.8 cm. Given that the rest length for the spring is 12.8 cm, what is the spring constant for the spring?