Physics P Worksheet 6.2 Circular Motion

Worksheet 6.2 Circular Motion

1. A 615–kg race car completes one lap at a constant speed in 14.3 s around a circular track with a

radius of 50 m. a. What is the acceleration of the car? b. What force does the track exert on the tires to allow the car to produce this acceleration?

2. An athlete whirls a 7 kg hammer 1.8 m from the axis of rotation in a horizontal circle. What is the tension in the chain if the hammer makes one rotation each second?

3. A jet flies in a circular path at a constant speed of 120 m/s. What is the smallest radius the pilot can fly if the acceleration does not exceed 7g?

4. Mike whirls a 0.20 kg stone at the end of a 30 cm long string in a horizontal plane above his head 2.05 m off the ground. At a certain instant the string breaks and the stone lands on the ground 18.5 m from the boy. a. Find the velocity of the stone just before the string broke b. Find the tension in the string just before it broke.

5. A space station is constructed in the shape of a doughnut whose outer diameter is 240 m. a. At what rate should this space station rotate so that its occupants will experience an acceleration

of g when they are at the outer diameter of the station? b. By what percentage will the weight of an individual change as he moves from the outer to the

inner part of the doughnut which has a radius of 200 m? 6. Assume that Earth is a perfect sphere of radius 6400 km, rotating about its axis once in 24 h, and that

at a pole the acceleration of gravity is exactly 9.81 m/s2. Determine the downward acceleration of a body in freefall at the equator.

7. Earth orbits the sun at a distance of 1.49 × 1011 m. a. What is the acceleration of Earth as it orbits the sun? b. If Earth has a mass of 5.95 × 1024 kg, what is the force exerted on Earth by the sun?

Physics P Worksheet 6.2 Circular Motion 1a. 𝑣 = !!

!!

𝑣 = !"!!

𝑣 = !" !"  !!".!  !

𝑣 = 22.0  m/s 𝑎 = !!

!

𝑎 = !!.!  !/! !

!"  !

𝑎 = 9.7  m/s! 1b. 𝐹! = 𝑚𝑎! 𝐹! = 615  kg 9.7  m/

s! 𝐹! = 5900  N 2. 𝐹! = 𝑚𝑎! 𝐹! =

!!!

!

𝐹! =! !!"

!

!

!

𝐹! =!!!!"!!

𝐹! =!!! !  !" !.!  !

!  ! !

𝐹! = 500  N 3. 𝑎 = !!

!

𝑟 =𝑣!

a

𝑟 =120  m/s !

7 ∙ 9.8  m/s!

𝑟 = 210  m

4a. 𝑡 = !!!

𝑡 = ! !.!"  !!

𝑡 = 0.647  s

𝑣 =∆d∆t

𝑣 =18.5  m0.647  s

𝑣 = 28.6  m/s

4b. 𝐹! =!!!

!

𝐹! =!.!"  !" !".!  !/! !

!.!"  !

𝐹! = 550  N 5a. 𝑎 = !!

!

𝑣 = 𝑎𝑟 𝑣 = 𝑔 240  m 𝑣 = 48.5  m/s 𝑣 = !"!

!

𝑇 = !"!!

𝑇 = !" !"#  !!".!  !/!

𝑇 = 31  s

5b. !!""#$!!!"#$

=!!!!!!""#$

!!!!!!!!"#$%

!!

!!""#$!!"#$%

= !!""#$!!"#$%

!!""#$!!"#$%

= !""  !!"#  !

!!""#$!!"#$%

= 0.83 = 83% 6. 𝑣 = !"!

!

𝑣 = !" !  !""  !!!  !!"  !""  !

𝑣 = 465  m/s 𝑎 = !!

!

𝑎 = !"#  !/! !

!  !""  !!!  !

𝑎 = 0.034  m/𝑠! 𝑔 = 9.81  m/𝑠! −

0.034  m/𝑠! 𝑔 = 9.78  m/𝑠! 7a. 𝑣 = !"!

!

𝑣 = !" !.!"  ×  !"!!  !!"  !!"  !!!  !

𝑣 = 29  700  m/s 𝑎 = !!

!

𝑎 = !"  !""  !/! !

!.!"  ×  !"!!  !

𝑎 = 0.0059  m/𝑠! 7b. 𝐹 = 𝑚𝑎 𝐹 =

5.95  ×  10!"  kg 0.0059  m/𝑠!

𝐹 = 3.5  ×  10!!  N