1. No category

5-42. Before 1960, it was believed that the maximum attainable coefficient of static friction for
an automobile tire was less than 1. Then, around 1962, three companies independently
developed racing tires with coefficients of 1.6. Since then, tires have improved, as illustrated in
this problem. According to the 1990 Guinness Book of Records, the fastest time interval for a
piston-engine car initially at rest to cover a distance of one-quarter mile is 4.96 s. Shirley
Muldowney set this record in September 1989. What minimum value of μs is necessary to
achieve the record time interval?
[Ans]
[註] 車子可以前進，是靠引擎帶動輪胎，向後推地面，而地面將車子往前推，摩擦力
就是中間的力，如果沒有摩擦力，馬力再大的車也無法前進。
5-49. A 9.00-kg hanging object is connected, by a light, inextensible cord over a light,
frictionless pulley, to a 5.00-kg block that is sliding on a flat table. Taking the coefficient of
kinetic friction as 0.200, find the tension in the string.
[Ans]
[註] 再做一次 Atwood’s machine 的題目，現在減緩加速度的是摩擦力而非重力。

5-63. A crate of weight Fg is pushed by a force P on a horizontal floor as shown in Figure P5.63.

The coefficient of static friction is μs, and P is directed at angle θ below the horizontal. (a)
µ F sec θ
Show that the minimum value of P that will move the crate is given by P = s g
1 − µ s tan θ
Figure P5.63
(b) Find the condition on θ in terms of μs for which motion of the crate is impossible for any
value of P.
[Ans]
(a) The crate is in equilibrium, just before it starts to move. Let the normal force acting on it
be n and the friction force, fs. Resolving vertically: n = Fg + P sin θ
and horizontally:
But, fs ≤ µsn,
Divide by cos θ.
Then Pminimum =
(b)
P cos θ = fs
i.e., P cos θ ≤ µs (Fg+ P sin θ) or P (cos θ − µs sin θ) ≤ µsFg
P (1 − µs tan θ) ≤ µsFg sec θ.
µ s Fg secθ
1 − µ s tan θ
To set the crate into motion, the x component (P cos θ) must overcome friction fs = µsn:
P cos θ ≥ µsn = µs (Fg + P sin θ)
P(cos θ − µs sin θ) ≥ µsFg
For this condition to be satisfied, it must be true that
(cos θ − µ s sin θ ) > 0 → µ s tan θ < 1 → tan θ <
If this condition is not met, no value of P can move the crate.
1
µs
.