Two identical horizontal springs are attached to opposite sides of a box that sits on a frictionless table. The outer ends of the springs are clamped while the springs are at their equilibrium lengths. Then a force applied to the box, parallel to the springs, compresses one spring by while stretching the other by the same amount. What is the spring constant of the springs?
The value of spring constant is .
Hooke's law says the force applied on spring is directly proportional to deformation in the spring.
Here, is force applied on spring, is spring constant, is deformation in the spring.
As we know two springs are identical therefore, spring constant for both springs is same.
Total deformation in spring is
Use Hooke's law
The gravitational attraction between two objects with masses and , separated by distance x, is , where G is the gravitational constant.
a. How much work is done by gravity when the separation changes from to ? Assume .
b. If one mass is much greater than the other, the larger mass stays essentially at rest while the smaller mass moves toward it. Suppose a comet is passing the orbit of Mars, heading straight for the sun at a speed of What will its speed be when it crosses the orbit of Mercury? Astronomical data are given in the tables at the back of the book, and .
Six dogs pull a two-person sled with a total mass of . The coefficient of kinetic friction between the sled and the snow is . The sled accelerates at until it reaches a cruising speed of . What is the team’s
(a) maximum power output during the acceleration phase and
(b) power output during the cruising phase?
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