A spring gun consists of a spring inside a plastic tube with spring constant, k. The spring can be compressed 20 cm from its equ ilibrium length. A 100 g hard plastic ball is then loaded into the tube. If the ball is shot directly up and reaches a height of 2 m above the top of the tube, what is the spring constant, k? Ignore air resistance.
1 answer:
Answer: The spring constant is K=392.4N/m
Explanation:
According to hook's law the applied force F will be directly proportional to the extension e produced provided the spring is not distorted
The force F=ke
Where k=spring constant
e= Extention produced
h=2m
Given that
e=20cm to meter 20/100= 0.2m
m=100g to kg m=100/1000= 0.1kg
But F=mg
Ignoring air resistance
assuming g=9.81m/s²
Since the compression causes the plastic ball to poses potential energy hence energy stored in the spring
E=1/2ke²=mgh
Substituting our values to find k
First we make k subject of formula
k=2mgh/e²
k=2*0.1*9.81*2/0.1²
K=3.921/0.01
K=392.4N/m
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