BackA spring of negligible mass has force constant N/m. You place the spring vertically with one end on the floor. You then drop a -kg book onto it from a height of m above the top of the spring. Find the maximum distance the spring will be compressed.
A spring of negligible mass has force constant N/m. How far must the spring be compressed for J of potential energy to be stored in it?
As a 15,000 kg jet plane lands on an aircraft carrier, its tail hook snags a cable to slow it down. The cable is attached to a spring with spring constant 60,000 N/m. If the spring stretches 30 m to stop the plane, what was the plane's landing speed?
A spring ( k = 75 N/m) has an equilibrium length of 1.00 m. The spring is compressed to a length of 0.50 m and a mass of 2.0 kg is placed at its free end on a frictionless slope which makes an angle of 41° with respect to the horizontal (Fig. 8–41). The spring is then released. Now the incline has a coefficient of kinetic friction μₖ. If the block, attached to the spring, is observed to stop just as it reaches the spring’s equilibrium position, what is the coefficient of friction μₖ?
(II) The spring of Problem 71 has a stiffness constant k = 160 N/m. The mass m = 6.0 kg is released from rest when the spring is stretched x0 = 1.0 m from equilibrium. Determine the total energy of the system.
(III) A spring ( k = 75 N/m) has an equilibrium length of 1.00 m. The spring is compressed to a length of 0.50 m and a mass of 2.0 kg is placed at its free end on a frictionless slope which makes an angle of 41° with respect to the horizontal (Fig. 8–41). The spring is then released. If the mass is not attached to the spring, how far up the slope will the mass move before coming to rest?
A spring ( k = 75 N/m) has an equilibrium length of 1.00 m. The spring is compressed to a length of 0.50 m and a mass of 2.0 kg is placed at its free end on a frictionless slope which makes an angle of 41° with respect to the horizontal (Fig. 8–41). The spring is then released. If the mass is attached to the spring, how far up the slope will the mass move before coming to rest?
Chris jumps off a bridge with a 15-m-long bungee cord (a heavy stretchable cord) tied around his ankle, Fig. 8–37. He falls 15 m before the bungee cord begins to stretch. Chris’s mass is 75 kg and we assume the cord obeys Hooke’s law, F = -kx with k = 55 N/m. If we neglect air resistance, estimate what distance d below the bridge Chris’s foot will be before coming to a stop. Ignore the mass of the cord (not realistic, however) and treat Chris as a particle.
A 50 g ice cube can slide up and down a frictionless 30° slope. At the bottom, a spring with spring constant 25 N/m is compressed 10 cm and used to launch the ice cube up the slope. How high does it go above its starting point?
A 1400-kg car moving on a horizontal surface has speed v = 85 km/h when it strikes a horizontal coiled spring and is brought to rest in a distance of 2.2 m. What is the spring constant of the spring? Ignore any thermal energy produced in the collision.
If you stand on a bathroom scale, the spring inside the scale compresses 0.60 mm, and it tells you your weight is 760 N. Now if you jump on the scale from a height of 1.0 m, what does the scale read at its peak? Assume Hooke’s law holds.
A stretched spring stores 2.0 J of energy. How much energy will be stored if the spring is stretched three times as far?
The ice cube is replaced by a 50 g plastic cube whose coefficient of kinetic friction is 0.20. How far will the plastic cube travel up the slope? Use work and energy.