View source for Giancoli Physics (5th ed) Chapter 2

==Problems==
[[Giancoli Physics (5th ed) Solutions | Return to Solutions]]
== Problems ==

===1. What force is needed to accelerate a child on a sled (total mass = 60.0 kg) at 1.15 m/s/s?===
:Assuming there is no friction, the any force we exert horizontally will be unbalanced, and so:
:F = ma
:F = (60.0 kg)(1.15 m/s/s) = 69 N
[[#top | Table of Contents]]
----

===2.===
[[#top | Table of Contents]]
----

===3. How much force is required to accelerate a 9.0-g object at 10,000 "g's" (say in a centrifuge)?=== 
:They give us m = 9.0 g = 9.0 x 10<sup>-3</sup> kg, and a = 10,000 "g's" = 98000 m/s/s so:
:F = ma = (9.0 x 10-3 kg)(98000 m/s/s) = 882 N = 880 N
[[#top | Table of Contents]]
----

===4. ===
[[#top | Table of Contents]]
----

===5. What is the weight of a 66-kg astronaut (a) on Earth, (b) on the moon (g = 1.7 m/s²), (c) on Mars (g = 3.7 m/s²), (d) in outer space traveling at constant velocity?=== 
:Weight (the force of gravity that causes the gravitational acceleration must equal ma because of Newton's second law:
:on earth  F = ma = (66 kg)(9.80 m/s/s) = 646.8 N = 650 N
:on moon F = ma = (66 kg)(1.7 m/s/s)   = 112.2 N = 110 N
:on mars  F = ma = (66 kg)(3.7 m/s/s)   = 244.2 N = 240 N
:At a constant velocity in space: F = ma = (66 kg)(0) = 0 N = 0 N
:(Since the velocity is constant, there is no acceleration so they are weightless)
[[#top | Table of Contents]]
----

===6. ===
[[#top | Table of Contents]]
----
===7. What average force is required to stop an 1100-kg car in 8.0 s if it is traveling at 90 km/h?===
:First, notice that the initial velocity is given in km/hr, so let's first change that to m/s by dividing by 3.6:
::90 km/hr/3.6 = 25 m/s
:We have a cute linear kinematics problem to solve:
:s = don't care
:u = 90 km/hr/3.6 = 25 m/s
:v = 0
:a = ???
:t = 8.0 s 

:Use v = u + at to find a:
:v = u + at
:0 = 25 m/s + a(8.0 s)
:a = -3.125 m/s/s
:so now we can use Newton's second law
:F = ma = (1100 kg)(-3.125 m/s/s) = -3437.5 N = -3400 N
[[#top | Table of Contents]]
----
===8. ===
[[#top | Table of Contents]]
----
===9. A fisherman yanks a fish out of the water with an acceleration of 4.5 m/s<sup>2</sup> using very light fishing line that has a "test" value of 22 N.  The fisherman unfortunately loses the fish as the line snaps.  What can you say about the mass of the fish? ===
:The weight of the fish is F = ma = mg down (-) and there is a possible force of 22 N up (+), so our expression of Newton's second law looks like this (up is +)  The acceleration of 4.5 m/s/s is also positive because it is up:
:<22 N - mg> = m(+4.5 m/s/s)
:<22  - 9.8m> = m(4.5)
:22 = 9.8m + 4.5m = 14.3m
:m = 22/14.3 = 1.538 kg = 1.5 kg
[[#top | Table of Contents]]
----

===10. ===
[[#top | Table of Contents]]
----

===11. What is the average force exerted by a shot-putter on 7.0-kg shot if the shot is moved through a distance of 2.8 m and is released with a speed of 13 m/s? ===

:We have a cute linear kinematics problem to solve first:
:s = 2.8 m
:u = 0 (assumed)
:v = 13 m/s
:a = ???
:t = Don't care 

:Use v2 = u2 + 2as,  a = 30.1786 m/s/s
:F = ma = (7.0 kg)(30.1786 m/s/s) = 211.25 = 210 N
[[#top | Table of Contents]]
----
===12. ===
[[#top | Table of Contents]]
----
===13. A 10-kg bucket is lowered by a rope in which there is 63 N of tension.  What is the acceleration of the bucket?  Is it up or down? ===

:First calculate the weight:
:F = ma = (10 kg)(9.80 m/s/s) = 98 N 

:Now you have a force of 98 N down (-) and a force of 63 N up (+) and our F = ma looks like this if we make up  positive:
:<63 N - 98 N> = (10 kg) a
:a = -3.5 m/s/s (down)
[[#top | Table of Contents]]
----
===14. ===
[[#top | Table of Contents]]
----
===15. A 75-kg petty thief wants to escape from a third-story jail window,  Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg.  How might the thief use this "rope" to escape?  Give quantitative answer.=== 

:If it can support a mass of 58 kg, the breaking force is the weight of 58 kg or (58 kg)(9.80 N/kg) = 568.4 N.  This would be the maximum upward force the sheets could supply.
:Mr. thief could accelerate downward at a constant rate, thereby reducing the tension in the sheets to this value.  So the thief would have 568.4 N of force upward (+), and his own weight (75 kg)(9.80N/kg) = 735 N down (-) and our F = ma looks like:
:<568.4 N - 735 N> = (75 kg)a
:a = -2.2213 m/s/s = -2.2 m/s/s.  By accelerating downwards at 2.2 m/s/s
[[#top | Table of Contents]]
----

===16. ===
[[#top | Table of Contents]]
----
===17. The cable supporting a 2100-kg elevator has a maximum strength of 21,750 N.  What maximum upward acceleration can it gave the elevator without breaking? ===
:First calculate the weight:
:F = ma = (2100 kg)(9.80 m/s/s) = 20580 N

:Now you have a force of 20580 N down (-) and a force of 21750 N up (+) and our F = ma looks like this if we make up  positive:
:<21750 N - 20580 N> = (2100 kg) a
:a = +.557 m/s/s = +.56 m/s/s upward
[[#top | Table of Contents]]
----

===18.===
[[#top | Table of Contents]]
----
===19.===
[[#top | Table of Contents]]
----
===20.===
[[#top | Table of Contents]]
----
===21.===
[[#top | Table of Contents]]
----
===22.===
[[#top | Table of Contents]]
----
===23.===
[[#top | Table of Contents]]
----
===24.===
[[#top | Table of Contents]]
----
===25.===
[[#top | Table of Contents]]
----
===26.===
[[#top | Table of Contents]]
----
===27.===
[[#top | Table of Contents]]
----
===28.===
[[#top | Table of Contents]]
----
===29.===
[[#top | Table of Contents]]
----
===30.===
[[#top | Table of Contents]]
----
===31.===
[[#top | Table of Contents]]
----
===32.===
[[#top | Table of Contents]]
----
===33.===
[[#top | Table of Contents]]
----
===34.===
[[#top | Table of Contents]]
----
===35.===
[[#top | Table of Contents]]
----
===36.===
[[#top | Table of Contents]]
----
===37.===
[[#top | Table of Contents]]
----
===38.===
[[#top | Table of Contents]]
----
===39.===
[[#top | Table of Contents]]
----
===40.===
[[#top | Table of Contents]]
----
===41.===
[[#top | Table of Contents]]
----
===42.===
[[#top | Table of Contents]]
----
===43.===
[[#top | Table of Contents]]
----
===44.===
[[#top | Table of Contents]]
----
===45.===
[[#top | Table of Contents]]
----
===46.===
[[#top | Table of Contents]]
----
===47.===
[[#top | Table of Contents]]
----
===48.===
[[#top | Table of Contents]]
----
===49.===
[[#top | Table of Contents]]
----
===50.===
[[#top | Table of Contents]]
----
===51.===
[[#top | Table of Contents]]
----
===52.===
[[#top | Table of Contents]]
----
===53.===
[[#top | Table of Contents]]
----
===54.===
[[#top | Table of Contents]]
----
===55.===
[[#top | Table of Contents]]
----
===56.===
[[#top | Table of Contents]]
----
===57.===
[[#top | Table of Contents]]
----
===58.===
[[#top | Table of Contents]]
----
===59.===
[[#top | Table of Contents]]
----
===60.===
[[#top | Table of Contents]]
----
===61.===
[[#top | Table of Contents]]
----
===62.===
[[#top | Table of Contents]]
----
===63.===
[[#top | Table of Contents]]
----
===64.===
[[#top | Table of Contents]]
----
===65.===
[[#top | Table of Contents]]
----
===66.===
[[#top | Table of Contents]]
----
===67.===
[[#top | Table of Contents]]
----
===68.===
[[#top | Table of Contents]]
----
===69.===
[[#top | Table of Contents]]
----
===70.===
[[#top | Table of Contents]]
----
===71.===
[[#top | Table of Contents]]
----
===72.===
[[#top | Table of Contents]]
----
===73.===
[[#top | Table of Contents]]
----
===74.===
[[#top | Table of Contents]]
----
===75.===
[[#top | Table of Contents]]
----
===76.===
[[#top | Table of Contents]]
----
===77.===
[[#top | Table of Contents]]
----
===78.===
[[#top | Table of Contents]]
----
===79.===
[[#top | Table of Contents]]
----
===80.===
[[#top | Table of Contents]]
----
===81.===
[[#top | Table of Contents]]
----
===82.===
[[#top | Table of Contents]]
----
===83.===
[[#top | Table of Contents]]
----
===84.===
[[#top | Table of Contents]]
----
===85.===
[[#top | Table of Contents]]
----
===86.===
[[#top | Table of Contents]]
----
===87.===
[[#top | Table of Contents]]
----
===88.===
[[#top | Table of Contents]]
----
===89.===
[[#top | Table of Contents]]
----
===90.===
[[#top | Table of Contents]]
----
===91.===
[[#top | Table of Contents]]
----
===92.===
[[#top | Table of Contents]]
----
===93.===
[[#top | Table of Contents]]
----
===94.===
[[#top | Table of Contents]]
----
===95.===
[[#top | Table of Contents]]
----
===96.===
[[#top | Table of Contents]]
----
===97.===
[[#top | Table of Contents]]
----
===98.===
[[#top | Table of Contents]]
----
===99.===
[[#top | Table of Contents]]
----
===100.===
[[#top | Table of Contents]]
----