Practice 4C: | 1 | 2 | 3 | Go up
Coefficients of friction- by Krista Heim, 2001

1. Once the crate in sample problem 4C is in motion, a horizontal force of 53 N keeps the crate moving with a constant velocity.  Find ต_{k, the coefficient of kinetic friction, between the crate and the floor.}  

Here's what you know, m=24 kg, F_f=53 N, g=9.8 m/s^2, use the formula F_g = mg,   F_g=24*9.8, solve for F_g, F_g=235.2 N, then use the formula F_f = ต_kF_n, 53=235.2ต_k, solve for ต_k, ต_k=.23
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2.   A 25 kg chair initially at rest on a horizontal floor requires a 365 N horizontal force to set it in motion.  Once the chair is in motion, a 327 N horizontal force keeps it moving at a constant velocity.  

        A.  Find the coefficient of static friction between the chair and the floor.  

        Here's what you know, m=25 kg, F_f=365 N, g=9.8 m/s^2, use the formula F_g = mg, F_g =25*9.8, F_g =245 N, then use the formula F_f <= ต_sF_n, 365=245ต_s, solve for ต_s,  ต_s=1.5.

        B.  Find the coefficient of kinetic friction between the chair and the floor.   

Here's what ya know, m=25 kg, F_f=327 N, the normal force of gravity will be the same as in part A.  Now use the formula F_f = µ_kF_n, 327=245 µ_k, solve for µ_k, µ_k=1.3.
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3.  A museum curator moves artifacts into place on many different display surfaces.  Use the values in Table 4-2 to find the max force of static friction and the force of kinetic friction for the following situations:

        A.  moving a 145 kg aluminum sculpture across a horizontal steel platform

        Here's what you know, m=145 kg, ต_s =.61, ต_k=.47, g= 9.8 m/s^2, find the normal force by using the formula F_g = mg, F_g=145*9.8, solve,     F_g=1421 N, now use F_f <= ต_sF_n, Static F_f =.61*1421, solve, Static F=870 N, then use F_f = ต_kF_n, Kinetic F_f= .47*1421, solve, Kinetic F=670 N. 

        B.  pulling a 15 kg steel sword across a horizontal steel shield

        Here's what you know, m=15 kg, ต_s =.74, ต_k=.57, g= 9.8 m/s^2, find the normal force by using the formula F_g = mg, F_g=15*9.8, solve,     F_g=147 N, now use F_f <= ต_sF_n, Static F_f =.74*147, solve, Static F=110 N, then use F_f = ต_kF_n, Kinetic F_f= .57*147, solve, Kinetic F=84 N.

        C.  pushing a 250 kg wood bed on a wood floor

        Here's what you know, m=250 kg, ต_s =.4, ต_k=.2, g= 9.8 m/s^2, find the normal force by using the formula F_g = mg, F_g=250*9.8, solve,     F_g=2450 N, now use F_f <= ต_sF_n, Static F_f =.4*2450, solve, Static F=1000 N, then use F_f = ต_kF_n, Kinetic F_f= .2*2450, solve, Kinetic F=500 N.

        D.  sliding a .55 kg glass amulet on a glass display case  

Here's what you know, m=.55 kg, ต_s =.9, ต_k=.4, g= 9.8 m/s^2, find the normal force by using the formula F_g = mg, F_g=.55*9.8,solve, F_g=5.39 N, now use F_f <= ต_sF_n, Static F_f =.9*5.39, solve, Static F=5 N, then use F_f = ต_kF_n, Kinetic F_f= .4*5.39, solve, Kinetic F=2 N.
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