Question

1. consider the crate on the incline in example problem 5. calculate the magnitude of the acceleration. after 4.00 s, how fast will the crate be moving?
2. jorge decides to try the slide discussed in example problem 6. jorges trip down the slide is quite different from ichikos. after giving himself a push to get started, jorge slides at a constant speed. what is the coefficient of kinetic friction between jorges pants and the slide?
3. stacie, who has a mass of 45 kg, starts down a slide that is inclined at an angle of 45° with the horizontal. if the coefficient of kinetic friction between stacies shorts and the slide is 0.25, what is her acceleration?
4. challenge you stack two physics books on top of each other as shown in figure 19. you tilt the bottom book until the top book just begins to slide. you perform five trials and measure the angles given in table 3.

a. what is the average φ measured during the five trials?
b. what is the coefficient of static friction between the covers of the two books? use the average φ found in part a.
c. you measure the top books acceleration down the incline to be 1.3 m/s². what is the coefficient of kinetic friction? assume φ is the average value found in part a.

Explanation:

Problem 35

Step1: Identify forces along incline

Gravity component: $mg\sin\theta$; friction: $\mu_k mg\cos\theta$

Step2: Apply Newton's second law

$ma = mg\sin\theta - \mu_k mg\cos\theta$ → $a = g(\sin\theta - \mu_k \cos\theta)$

Step3: Substitute values

$g=9.8m/s^2$, $\theta=45^\circ$, $\mu_k=0.25$
$\sin45^\circ=\cos45^\circ=\frac{\sqrt{2}}{2}\approx0.7071$
$a=9.8(0.7071 - 0.25×0.7071)=9.8×0.7071×0.75$

Step4: Calculate acceleration

$a≈9.8×0.5303≈5.2m/s^2$

Step1: Sum all angles

$21^\circ + 17^\circ + 21^\circ + 18^\circ + 19^\circ = 96^\circ$

Step2: Divide by number of trials

Average $\phi=\frac{96^\circ}{5}=19.2^\circ$

Step1: Condition for impending slide

$\mu_s = \tan\phi$

Step2: Substitute average $\phi$

$\mu_s = \tan(19.2^\circ)≈0.35$

Answer:

$5.2m/s^2$

Problem 36a