Question

When a 3.0-kg block is pushed against a massless spring of force constant 4.5 × 10³ N/m, the spring is compressed 8.0 cm. The block is released, and it slides 2.0 m (from the point at which it is released) across a horizontal surface before friction stops it. What is the coefficient of kinetic friction between the block and the surface?

Solution

Verified
Step 1
1 of 2

In this problem we consider a block of mass m=3m=3 kg which compresses a horizontal spring of constant k=4.5103k=4.5\cdot10^3 N/m by x=8x=8 cm. The initial energy stored in the spring is equal to

Es=12kx2=12(4.5103 N/m)(0.08 m)2=14.4 J.\begin{align*} E_{s}&=\frac{1}{2}kx^2\\ &=\frac{1}{2}(4.5\cdot10^3\text{ N/m})\cdot(0.08\text{ m})^2\\ &=14.4\text{ J}. \end{align*}

This is the total energy of the system, and the friction does work to stop the block after d=2d=2 m. The work done is therefore equal to the initial energy in the spring, which gives the friction coefficient

Wfric=EsFfricd=EsμKmgd=EsμK=Esmgd=14.4 J(3 kg)(9.81 m/s2)(2 m)=0.24.\begin{align*} W_{fric}&=E_s\\ F_{fric}d&=E_s\\ \mu_Kmgd&=E_s\\ \mu_K&=\frac{E_s}{mgd}\\ &=\frac{14.4\text{ J}}{(3\text{ kg})\cdot(9.81\text{ m/s}^2)\cdot(2\text{ m})}\\ &=\boxed{\color{#c34632}0.24.} \end{align*}

Create a free account to view solutions

Create a free account to view solutions

Recommended textbook solutions

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics 4th Edition by Randall D. Knight

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

4th EditionISBN: 9780133942651 (1 more)Randall D. Knight
3,507 solutions
Mathematical Methods in the Physical Sciences 3rd Edition by Mary L. Boas

Mathematical Methods in the Physical Sciences

3rd EditionISBN: 9780471198260Mary L. Boas
3,355 solutions
Fundamentals of Physics 10th Edition by David Halliday, Jearl Walker, Robert Resnick

Fundamentals of Physics

10th EditionISBN: 9781118230718 (2 more)David Halliday, Jearl Walker, Robert Resnick
8,971 solutions
University Physics, Volume 1 1st Edition by Jeff Sanny, Samuel J Ling, William Moebbs

University Physics, Volume 1

1st EditionISBN: 9781938168277Jeff Sanny, Samuel J Ling, William Moebbs
1,471 solutions

More related questions

1/4

1/7