A spring has a spring stiffness constant k of 85.0 N/m . How much must this spring be compressed to store 25.0 J of potential energy

Explanation:

We know that the expression for the energy stored in a spring is given as

E= 1/2kx²

Given data

K=85N/m

E=25j

Substituting we have

25= 1/2(85)*x²

2*25=85x²

x²=50/85

x²=0.588

x=√0.588

x=0.76m

the spring must be compressed to 0.76m

given data:

determine the horse power (h.p) = ?

force applied to move the box(f) = 10 pounds,

box lifted from a distance         (d) = 3 feet

time taken to lift                         (t) = 10 sec,

the horse power is defined as amount of work required to move a load. the horse power is equal to 550 foot-pound per second

                  1 h.p   = 550 foot-pound/second

it can also be defined as the the load that need to be move a body for certain distance in a certain amount of time.

mathematically,

                      h.p = (force × distance)/ time

                            = (10 × 3)/ 10

                            = 30/10

                            = 3 foot -pound/sec

hence, the horse power is needed to move the box is 3 foot-pound/second

important note: 1 h.p = 550 foot-pound/second = 746 watts

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hope this !