Law of Inertia          (back to the questions)         (back to the top)

1.  The motion of an object does not change unless it is acted on by a non-zero external force.

2.  All of the forces are internal; your hands pull up on the rope, your feet push down on the
     rope.  The total force on the rope is zero, it doesn’t move; you don’t move.

3.  Left, no. (forces add to zero)         Right, yes. (forces create a non-zero total force)

4.  a)  yes, motion is changing
    b)  No, force of gravity acts at a right angle to the motion

5.  a) Yes, car is changing direction.
     b) yes, the force comes from friction with the ground.

6.  No, no change in motion means the total force is zero.

7.  The books are moving with the car when the brakes are applied .  When car stops,
     only friction with the seat can stop the books.  Guess it isn’t enough.

8.  If you are belted in the seat, when the plane goes down, you go down.  When you go down,
     the glass goes down.  There is nothing to make the soda go down.  The soda appears to fly
     up out of the container toward the ceiling.  Actually it is staying still while everything else falls.

9.  No.  When you are hit from behind the car moves forward.  The seat pushes your body
     forward.  Your head is left behind, so it moves back relative to your body.
 

Action / Reaction Forces  (back to the questions)        (back to the top)

1.  a) Foot hits ball / ball hits foot
     b) Shuttle engines push gases out the back / gases push shuttle forward
     c)  Earth pulls on you / you pull on the earth
     d) You push down on the ground / ground pushes up on you

2.  a) Friction between the tires and the road
     b) Tires push ground backward / ground push tires (and car) forward

3.  a)  No.  The action and reaction forces are equal.
     b) Since the car has less mass it will experience more acceleration for the same force
         (Newton’s 2nd law).  People in the car will experience more change in motion.
         It is the change in motion which causes the injuries.

4.  If your push on the cart is more than the frictional forces on the cart it will accelerate.

5.  No.  Only internal forces here.  Fan pushes on the air / air pushes on the sail.

6.  a) 2nd law.  Larger mass has smaller acceleration for the same force.
     b) 3rd law.  Gun pushes bullet forward / bullet pushes gun backward into shoulder.
     c) 1st law.  People continue to move when bus changes its motion.
 

Newton's Second Law             (back to the questions)         (back to the top)

1.  No.  2M will have 1/2 a for the same F.

2.  No.  2M needs 2 F for the same a.

3.  a)  No. The net force does not equal to zero.  F_A  > F_f
     b)  yes.  They are tied together.
     c)  Less.  First string has to accelerate two masses.  Second string only one.

4.  a)  No.  Force of gravity is the same on both sides, net force equals zero.
     b)  Equal to.  That’s the force pulling on each end.
     c)  No.  Now net force is not equal to zero, the system accelerates.

5.  a = F_T / M = 15.0 N /3.0 Kg  = 5.0 m/s²

6. F_T  = M a  =  0.030 Kg (7000 m/s² ) = 210 N

7.  a = F_T / M             F_T = pull - friction  = 30.0 N - 10.0 N = 20.0 N
       = 20.0 N / 4.0 Kg  =  5.0 m/s²

8.  F_g  = M g = 2.5 Kg (9.8 m/s² ) = 24.5 N

9.  a) F_T   = F_up  - F_g  = 35.0 N - 19.6 N = 15.4 N [up]

     b)  a = F_T  / M  =  15.4 N [up] / 2.0 Kg = 7.7 m/s² [up]
 

Newton's Laws and Motion              (back to the questions)         (back to the top)

1. 
 

2. 
 

3. 
 

4. 
 

5. 
 

Uniform Circular Motion      (back to the questions)        (back to the top)

1.  Car A                 2. Car B                    3.  f = 1 rev / 60 sec  = 0.017 hz

4.  toward the center of the circle (centripetal)

5.  a)  pushed into the door
     b)  No
     c) centripetal (toward the center)
     d) A

6.  F_c  = M V² /R  so  V = sqrt( F_c R / M)
    The speed depends on :

the friction with the road (F_c),
the radius of the curve (R),
and the mass of the car (M).

7.  At the lowest point;  T = F_c  + F_g

8.  a_c  = V²  / r = (1.5 m/s)²  / 0.65 m = 3.5 m/s²

9.  a)  a_c  = V²  / r = (5m/s)² / 20 m  = 1.25 m/s²

     b)  F_c  = M a_c  = 1500 Kg  (1.25 m/s² )  = 1875 N

     c)  frictional force between the elephant’s feet and the ground

     d)  elephants can’t skate  ( actually the frictional force would not be large enough)
 

10.    a)  V = 2 P r / T = 2 P 30.0 m / 20.0 s  = 9.42 m/s

        b)  a_c  = V² / r = (9.42 m/s)²  / 30.0 m  = 2.96 m/s²

        c)  No, there’s no M in the acceleration equation.

        d)  F_c  = M a_c  = 55 kg (2.96 m/s² )  = 163 N

        e) 
                  i)   F_c  = N + F_g (as vectors)
                        N  = F_c  - F_g  = 163 N[down] - 539 N[down]
                                             = - 377 N[down]
                                             = 377 N [up]
                  ii)  F_c  = N + F_g
                         N  = F_c  - F_g  = 163 N[up] - 539 N[down]
                                              =  163[up] + 539[up]    (remember, subtraction is the same
                                                                                                  as adding the opposite)
                                              =702 N [up]
 
 

11.  a)  a_c  = V² / r = (9.1 m/s)2 /5.0 m  = 16.6 m/s²

        b)  N = F_c  - F_g        F_c  = M a_c  = 996 N [down]             F_g  = 588 N [down]
                = 408 N [down]

        c)  No.  You feel pushed up, into the seat a little lighter than normal.

        d)   i)  No.  The larger massed rider will experience a larger force (Newton’s 2nd law)

             ii)  yes.  The forces are directly proportional to the masses when they have the same
                          accelerations as they do here.