Question

7) A 0.2 kg mass is dropped from a 10 m high building on top of a spring that is placed vertically. It stops after moving 9.2 meters down and stops 0.8 meters above the ground while compressing the spring by 0.5 meters. What is the spring coefficient if air resistance is negligible?

Answer 1

the spring coefficient is

k=16N/m

Step-by-step explanation:

Hooks law states that provided the elasticity of a material is not exceeded the extension e is proportional to the applied force

Step one

Analysis of the problem

From analysis of the problem

The mass has a potential energy due to the height it was dropped from, the potential energy is then stored in the spring since it was dropped on the spring which compresses it by 0.5m

Step two

Data

Mass of object m=0.2kg

Height of building =10m

Compression of spring e=0.5m

Spring constant k=?

Step three

According to the principle of energy conservation

mgh=1/2(k*e^2)

Making k subject of formula we have

k=2mgh/e^2

Substituting our data into the expression to get k

Assuming g=9.81m/s

k=2*0.2*10/0.5^2

k=4/0.25

k=16N/m