At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Our platform offers a seamless experience for finding reliable answers from a network of experienced professionals. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Answer:
the maximum distance = 3.75 cm
Explanation:
To find the maximum distance the spring can be stretched without the box moving when it is released, we have to find out all the forces that work on the box.
Refer to the picture, there are 4 forces work on the box:
- [tex]F_{spring}=\text{spring force}[/tex]
- [tex]f_s=\text{static force}[/tex]
- [tex]w=\text{weight}[/tex]
- [tex]N=\text{normal force}[/tex]
Given:
- [tex]\text{mass (m)}=0.50\ kg[/tex]
- [tex]\text{spring constant (k)}=68\ N/m[/tex]
- [tex]\text{coefficient of static friction }(\mu_s)=0.52[/tex]
By applying these formulas, we can find the distance:
[tex]\boxed{w=mg}[/tex]
[tex]\boxed{f_s=\mu_sN}[/tex]
[tex]\boxed{F_{spring}=kx}[/tex]
Since the box is in an equilibrium state (not moving), then:
- [tex]\Sigma F_y=0[/tex]
- [tex]\Sigma F_x=0[/tex]
[tex]\Sigma F_y=0[/tex]
[tex]N-w=0[/tex]
[tex]N=w[/tex]
[tex]N=mg[/tex]
[tex]N=0.50\times9.8[/tex]
[tex]N=4.9\ N[/tex]
[tex]\Sigma F_x=0[/tex]
[tex]F_{spring}-f_s=0[/tex]
[tex]kx-\mu_sN=0[/tex]
[tex]68x-0.52\times4.9=0[/tex]
[tex]x=2.548\div68[/tex]
[tex]x=0.0375\ m[/tex]
[tex]\bf x=3.75\ cm[/tex]
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.