physics questions

<p>Can somebody help me answer these questions (with work shown) pleasee?</p>

<ol>
<li><p>While chopping down his father's cherry tree, George discovered that if he swung the axe with a speed of 25m/s, it would embed itself 2.3 cm into the tree before coming to a stop.
a)if the axe head had a mass of 2.5 kg, how much force was the tree exerting on the axe head upon impact?
b) How much force did the axe exert back on the tree?</p></li>
<li><p>Rather than taking the stairs, Martin gets from the second floor of his house to the first floor by sliding down the banister that is inclined at an angle of 30.0 degrees to the horizontal.
a) If Martin has a mass of 45 kg and the coefficient of sliding friction between Martin and the banister is 0.20, what is the force of friction impeding Martin's motion down the banister?
b) If the banister is made steeper (inclined at a larger angle), will this have any effect on the force of friction? If so, what?</p></li>
<li><p>Howard, the soda jerk at Bea's dinner, slides a 0.60-kg root beer from the end of the counter to a thirsty customer. A force of friction of 1.2 N brings the drink to a stop right in front of the customer.
a) What is the coefficient of sliding friction between the glass and the counter?
b) If the glass encounters a sticky patch on the counter, will this spot have a higher or lower coefficient of friction?</p></li>
</ol>

<p>Thanks so much!</p>

<ol>
<li><p>a) v^2 = vi^2 + 2ad</p>

<pre><code>0 = 25^2 + 2a(.023m)

-625/2(.023) = 13587 m/s/s
</code></pre>

<p>F = ma = 2.5 kg x 13587 m/s/s = 33970 N</p>

<p>b) 33970 N; Newton’s 3rd Law (opposite and equal reaction)</p></li>
<li><p>a) F(normal) = mg cos angle</p>

<p>Fn = 45 kg x 9.8 m/s/s cos 30 = 382 N</p>

<p>F(friction) = Fn x coefficient of friction</p>

<p>Ff = 382 N x .20 = 76.4 N</p>

<p>b) The force of friction will be lower since the normal force will decrease due to the decrease in the cos angle part of the formula.</p></li>
<li><p>a) Ff = Fn x u (coeff of f)</p>

<p>u = Ff/Fn = 1.2 N / .6 kg x 9.8 m/s/s = .204</p>

<p>b) Higher; if the glass sticks to it, it can’t move.</p></li>
</ol>

<p>Thanks for your help but can I ask u three more questions? I’m really sorry…</p>

<ol>
<li><p>Carter’s favorite ride at Playland Amusement Park is the rollercoaster. The rollercoaster car and passengers have a combined mass of 1620 kg, and they descend the first hill at an angle of 45.0 degrees to the horizontal. With what force is the rollercoaster pulled down the hill?</p></li>
<li><p>A box of mass m1=1.5kg is being pulled by a horizontal string having tension T=90N. It slides with friction (mk=0.51) on top of a second box having mass m2=3kg, which in turn slides on a frictionless floor. What is the acceleration of the second box?</p></li>
<li><p>A box of mass m=10.21 kg is at rest on a floor. The coefficient of static friction between the floor and the box is ms=0.4. A rope is attached to the box and pulled at an angle of q= 30o above horizontal with tension T=40N. Does the box move?</p></li>
</ol>

<p>Thanks again! I really appreciate ur help!</p>

<p>1) F=ma
F=(1620kg)(sin 45)(9.8 m/s^2)
F=11226 N (Its 11200 N if you account for sig figs)</p>

<p>2) Ff=uk<em>Fn
Ff=.51</em>9.8m/s^2*1.5kg
Ff=7.497N
Fnet=90N-7.497N
Fnet=82.503N</p>

<p>Second box:
F=ma
82.503N=(3.0kg)(a)
a=18.334 m/s^2 (18 m/s^2 with sig figs)</p>

<p>I’m not completely confident about the 18 m/s^2 though.</p>

<p>3) Ff=9.8m/s^2<em>10.21kg</em>.4
Ff=40.0232N</p>

<p>Fp=cos(30)*40N
Fp=34.64N</p>

<p>But you need to account for the effect of the upward pull on the Fn and therefore Ff.</p>

<p>Ff=us<em>Fn
Ff=.4</em>(9.8m/s^2<em>10.21kg-cos30</em>40N)
Ff=26.167N</p>

<p>Yes, the box does move because Friction only exerts a force of 26.167N while the horizontal force of the pull is 34.64N.</p>