Aspring of negligible mass has force constant k =1600 n/m
(a) how far must the springbe compressed for 3.20 j of potential energy to be stored in it?
(b) you place the springvertically with one end on the floor. you then drop a 1.20-kg book onto it from a height of 0.80 m above the top of the spring. find the maximum distance the spring will becompressed.

(a)

m

(b)

m

Explanation:

(a)

= Potential energy stored in the spring = 3.20 J

= Spring constant of the spring = 1600 N m⁻¹

= Compression of the spring

Potential energy stored in the spring is given as

inserting the values

m

b)

= mass of the book being dropped = 1.20 kg

= height of the book being dropped above the top of spring = 0.80 m

= distance by which the spring gets compressed

Assuming the reference point for measuring the gravitational potential energy to be as the lowest point of the book after compression of the book.

Using conservation of energy

Spring Potential energy  = Potential energy of the book

Solving the quadratic equation, we get

m

(a) 6.32 cm

(b) 0.108 m

Explanation:

force constant, k = 1600 N/m

(a) Potential energy, U = 3.2 J

Let the spring is compressed by a distance d.

Use the formula for the potential energy of the spring

Substitute the values

3.2 = 0.5 x 1600 x d^2

d = 0.063 m = 6.32 cm

(b) mass of book, m = 1.2 kg

height, h = 0.8 m

The potential energy of the book is converted into the potential energy of the spring.

Let the maximum compression of the spring is y .

1.2 x 9.8 x 0.8 = 0.5 x 1600 x y^2

y = 0.108 m