Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Answer:
See the explanation below.
Explanation:
By means of Hooke's second law, we can calculate the spring constant with the initial conditions of the problem.
[tex]F=k*x[/tex]
where:
k = spring constant [N/m]
x = distance = 0.01 [m]
F = force or weight [N]
Weight can be calculated by means of the product of mass by gravitational acceleration.
m = mass = 500[g] = 0.5[kg]
[tex]W=F=m*g\\W = 0.5*9.81\\W= 4.905[N][/tex]
Now the spring constant can be calculated:
[tex]k=F/x\\k=4.905/0.01\\k = 490.5[N/m][/tex]
We must now use the same Hooke's law to determine the new spring force when stretching it 0.03 [m]
[tex]F_{new}=k*x\\F_{new}=490.5*0.03\\F_{new}=14.715[N][/tex]
Now we have to use Newton's second law to calculate acceleration. We must remember that Newton's Second Law tells us that the sum of forces is equal to the product of mass by acceleration.
[tex]F=m*a[/tex]
where:
F = Fnew = 14.715[N]
m = mass = 500 [g] = 0.5 [kg]
a = acceleration [m/s²]
Now replacing:
[tex]14.715=0.5*a\\a=14.715/0.5\\a=29.43[m/s^{2} ][/tex]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.