Answer:
1) the mass of the toy is 0.304 kg
2) the amplitude of the motion is 0.1524 m
3) the maximum speed obtained by the object during its motion is 4.87 m/s
Explanation:
Given the data in the question;
force constant of spring k = 310 N/m
position of toy x = 0.120 m
speed v = 3 m/s
Total energy E = 3.6 J
let m represent mass of toy.
1.) Find the mass of the toy.
we know that; The total energy of the system equals the sum of kinetic energy of the toy and the potential energy of the spring;
E = [tex]\frac{1}{2}[/tex]kx² + [tex]\frac{1}{2}[/tex]mv²
we substitute
3.6 = ( [tex]\frac{1}{2}[/tex] × 310 × (0.120)² ) + ( [tex]\frac{1}{2}[/tex] × m × (3)² )
3.6 = 2.232 + 4.5m
3.6 - 2.232 = 4.5m
1.368 = 4.5m
m = 1.368 / 4.5
m = 0.304 kg
Therefore, the mass of the toy is 0.304 kg
2) Find the amplitude of the motion.
we know that;
E = [tex]\frac{1}{2}[/tex]kA²
where A is the amplitude of the motion,
we substitute
3.6 = [tex]\frac{1}{2}[/tex] × 310 × A²
3.6 = 155 × A²
A² = 3.6 / 155
A² = 0.0232258
A = √0.0232258
A = 0.1524 m
Therefore, the amplitude of the motion is 0.1524 m
3) Find the maximum speed obtained by the object during its motion;
we know that;
E = [tex]\frac{1}{2}[/tex]m[tex]v_{max[/tex]²
where [tex]v_{max[/tex] is the maximum speed
so we substitute
3.6 = [tex]\frac{1}{2}[/tex] × 0.304 × [tex]v_{max[/tex]²
3.6 = 0.152 × [tex]v_{max[/tex]²
[tex]v_{max[/tex]² = 3.6 / 0.152
[tex]v_{max[/tex]² = 23.6842
[tex]v_{max[/tex]² = √23.6842
[tex]v_{max[/tex]² = 4.8664 ≈ 4.87 m/s
Therefore, the maximum speed obtained by the object during its motion is 4.87 m/s
