Practice 4C: | 1 | 2 |
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**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_{k}F_{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_{s}F_{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_{k}F_{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_{s}F_{n},
Static F_{f} =.61*1421, solve, Static F=870 N,
then use F_{f} = ต_{k}F_{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_{s}F_{n},
Static F_{f} =.74*147, solve, Static F=110 N, then
use F_{f} = ต_{k}F_{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_{s}F_{n},
Static F_{f} =.4*2450, solve, Static F=1000 N,
then use F_{f} = ต_{k}F_{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_{s}F_{n}, Static F_{f}=.9*5.39, solve, Static F=5 N, then use F_{f}= ต_{k}F_{n}, Kinetic F_{f}= .4*5.39, solve, Kinetic F=2 N.

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