g68s4cgptg
Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

A spring lies on a horizontal table, and the left end of the spring is attached to a wall. The other end is connected to a box. The box is pulled to the right, stretching the spring. Static friction exists between the box and the table, so when the spring is stretched only by a small amount and the box is released, the box does not move. The mass of the box is 0.50 kg, and the spring has a spring constant of 68N/m. The coefficient of static friction between the box and the table on which it rests is μs 0.52. How far can the spring be stretched from its unstrained position without the box moving when it is released?

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]

View image karmenchong
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.