Spring A of stiffness 10 N/m is hung vertically from a ringstand. From the lower end of this spring, a different spring (Spring B) of stiffness 20 N/m is hung. And from the lower end of this spring, a 0.25-kg block is hung in equilibrium. When springs are connected in this orientation, they are said to be in series. Neglect the mass of the springs.
A certain tin wire (white tin, as opposed to gray tin) has a length of 1.5 m and a square rectangular cross section that is (1 mm x 1 mm). With a tension of 200 N applied to the wire, it stretches 6 mm. Use a simple ball-and-spring model of a solid, and assume that tin's crystal lattice is simple cubic, with atoms essentially stacked next to and on top of one another, like inflated basketballs stacked in a box. From these measurements, approximate the bond stiffness of tin. The density of white tin is . Its atomic weight is 118.7 g/mol.
Suppose that in the lab, you build a set of identical balls connected by identical springs, as shown below.
The masses of the balls and springs are negligible compared to the block that you hang from the apparatus. If you hang a 0.25-kg block in equilibrium, the apparatus stretches 0.050 m from its relaxed length.
A comet of mass orbits Sun which has a mass . Use the following constants and initial conditions for the comet in your calculations.
Assume that Sun remains stationary during the orbit (i.e. it does not "wobble").
A spring-loaded dart gun is used to shoot a 5-gram dart straight upward. Its spring has a stiffness 50 N/m, and its relaxed length is 5.0 cm. The spring is compressed 4.0 cm from its relaxed length. What is the velocity of the dart when it leaves the spring (i.e. at the instant the spring returns to its relaxed length)? Apply the Momentum Principle iteratively in order to answer the question.
In the lab, you connect one end of a 15 N/m spring to a ringstand, and you hang a 0.25-kg block from the other end of the spring. It hangs vertically in equilibrium.
The piece of exercise equipment shown below includes two handles that are on each end of two parallel springs, each with a stiffness 500 N/m. To build strength, a person holds the two handles and pulls them apart with equal magnitude forces applied in opposite directions to the handles, thus stretching the springs. Neglect the mass of the springs and assume that they are pulled horizontally.
A spring-loaded dart gun is used to shoot a 5-gram dart straight upward. Its spring has a stiffness 50 N/m, and its relaxed length is 5.0 cm. The spring is compressed 4.0 cm from its relaxed length.
A planet of mass kg is at a location m. A star of mass kg is at a location m. What is the gravitational force by the star on the planet?
The International Space Station orbits Earth at an altitude of about 350 km (from Earth's surface).