(263.1 years) x (half-life / 87.7 years) = 3 half-lifes
In 3 half-lifes, (1/2 x 1/2 x 1/2) = 1/8 of the atoms in a sample remain unchanged.
That's 12.5% that remain unchanged.
The other 87.5% of the atoms in the sample have decayed, and changed to either other isotopes of plutonium or into atoms of other elements.
Answer:
F₂= 210 pounds
Explanation:
Conceptual analysis
Hooke's law
Hooke's law establishes that the elongation (x) of a spring is directly proportional to the magnitude of force (F) applied to it, provided that said spring is not permanently deformed:
F= K*x Formula (1)
Where;
F is the magnitude of the force applied to the spring in Newtons (Pounds)
K is the elastic spring constant, which relates force and elongation. The higher its value, the more work it will cost to stretch the spring. (Pounds/inch)
x the elongation of the spring (inch)
Data
The data given is incorrect because if we apply them the answer would be illogical.
The correct data are as follows:
F₁ =80 pounds
x₁= 8 inches
x₂= 21 inches
Problem development
We replace data in formula 1 to calculate K :
F₁= K*x₁
K=( F₁) / (x₁)
K=( 80) / (8) = 10 pounds/ inche
We apply The formula 1 to calculate F₂
F₂= K*x₂
F₂= (10)*(21)
F₂= 210 pounds
The net force is the difference between upwards force and downwards force, so 53.7N-40N=13.7N=∑F. ∑F=ma, m=5.1kg, so a=13.7N/5.1kg.