A spring is used to stop a 50-kg package which is moving down a 20º incline. The spring has a constant k = 32 kN/m and is held by cables so that it is initially compressed 50 mm. Knowing that the velocity of the package is 2 m/s when it is 8 m from the spring and neglecting friction, determine the maximum additional deformation of the spring in bringing the package to rest.

Explanation:

The system formed by the spring and the package is described by the means of the Principle of Energy Conservation:

After expanding and symplifying the expression, a second-order polynomial is found:

The roots of the polynomial are:

Physically speaking, the first root is the only real solution.

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2