1.  A flying saucer moving initially at 20 m/s[E] accelerates to 50 m/s[W] in 3.8 s. Find the saucer’s average acceleration during the time interval.

2.   R.R. Hood is travelling to visit her grandmother. First, she travels at an average speed of

12 km/h for 10 km. Then she travels at 8.0 km/h for another 1.25 h. Calculate her            average speed for the entire trip to grandma’s house? (Don’t worry about the return trip -

she catches a ride with B.B. Wolf)

3.  A dog, initially sitting next to its owner, runs first to a position 2.8 m[W] of its owner, and then secondly to a position 12.6 m[E] of its owner.

a.   Draw a diagram showing the (i) position vectors and (ii) resultant displacement vector in this situation.

b.   Determine the dog’s total distance and total displacement.

4.

5.  A store clerk pushes a parcel along a counter with a force of 17.7 N[W]. The parcel has a mass of 2.5 kg. The kinetic friction acting on the parcel is 6.5 N[E].

a.   Draw a FBD of the parcel as it is being pushed. Be sure to label your forces appropriately and to include values.

b.   Calculate the net force acting on the parcel.

c.   Calculate the acceleration of the parcel.

d.   Determine the coefficient of kinetic friction between the parcel and the counter.

6.  Two crates, of mass 12.0 kg and 20.0 kg, respectively, are pushed across a smooth (ie no friction) floor together, the 12 kg crate in front of the 20 kg crate. Their acceleration is

3.50 m/s2 .

a.   Calculate the force applied to push the crates. Don’t forget to include a FBD.

b.   Calculate the action-reaction force between the two crates. Don’t forget to include FBD(s).

7.  A child’s wagon experiences a frictional force of 63 N whenever it is in motion,         regardless of the load it is carrying. An applied horizontal force of 128 N causes the wagon to accelerate at 5.0 m/s2 . The same applied force, with a child on the wagon, causes it to accelerate at 1.0 m/s2 .

a.  What is the mass of the sled? Don’t for  get to include a FBD.

b.  What is the mass of the child? Don’t forget include a FBD.

8.

9.  Assume that for each pulse, a human heart accelerates 2.1 × 10-2  kg of blood from 0.18 m/s2 to 0.28 m/s2 during a time interval of 0.10 s. Calculate the magnitude of:

a.  the acceleration of the blood

b.  the net force needed to cause that acceleration

10. An astronaut on the surface of Mars finds that a rock accelerates at 3.6 m/s2 when it is dropped. The astronaut also 2 finds that a force scale reads 260 N when the astronaut steps on it.

a.  What is the astronaut’s mass as determined on the surface of Mars?

b.  What would the force scale read if the astronaut stepped on it on Earth?

11. A sled, 14.0 kg in mass, is being towed over ice by a rope that makes an angle of 30.0° with the horizontal. A force of 236 N acts along the rope. The frictional force is 100 N.   Draw a FBD of the situation. Be sure to label your forces appropriately and to include   their values.

12. A skier weighing 300 N (ie F = 300 N) has just begun descending a 20° slope. The      coefficient of kinetic friction is 0.20. Draw a FBD of the situation. Be sure to label your g forces appropriately and to include their values.

13. A girl pushes a snow shovel weighing 30 N at a uniform velocity across a sidewalk. The handle of the shovel is inclined at 40° to the horizontal and she pushes along the handle with a force of 150 N.

a.   Draw a FBD of the situation. Be sure to label your forces appropriately and applied to include values.

b.  What is the coefficient of kinetic friction?

14. A 8.0 kg mass on a frictionless table is accelerated by a 2.0 kg mass hanging from the

table as shown.

a.   Draw a FBD for each mass. Be sure to label your forces appropriately and to include values (if possible).

b.   Calculate the acceleration of the blocks.

c.   Calculate the tension in the rope.

15. A cougar is crouched on the branch of a tree that is 3.82 m above the ground. He sees an unsuspecting rabbit on the ground, sitting 4.12 m from the spot directly below the    branch on which he is crouched. He jumps horizontally and lands on the rabbit.

a.   How long was the cougar in flight?

b.  What was the initial velocity of the cougar?

16. A beam of electrons (mass = 9.11 × 10-31  kg) is caused to move in a circular path of radius 3.00 m at a velocity of 2.00 × 107  m/s.

a.   Find the (i) centripetal acceleration and (ii) centripetal force acting on one electron.

b.  What type of force supplies the centripetal force?

17. While hiking in the wilderness, you come to the top of a cliff that is 80.0 m high. You throw a stone from the cliff, giving it an initial velocity of 27 m/s at 55° above the      horizontal.

a.  What are the horizontal and vertical components of the initial velocity?

b.   How long was the stone in flight?

c.   How far from the base of the cliff does the stone land?

18. A car exiting a freeway enters an icy curve (ie no friction) with a radius of curvature of

175 m is banked at 12° .

a.   Draw a FBD of the situation. Be sure to label your forces appropriately and to include values (if possible).

b.  At what speed (in km/h) must a car travel to ensure that it does not leave the road?

19. If the coefficient of friction between your running shoes and the gym floor is 0.90, what is the smallest circle (radius) that you could run at 6.2 m/s without slipping? Be sure to       include a FBD to help you analyze this problem!

20.

21. The force-deformation graph for a non-Hooke’s Law spring is shown below.

a.   How much work must be done to compress the spring 0.16 m?

b.   How much potential energy is stored in the spring at this compression?

c.   What speed would a 1.0 kg mass acquire if it were placed next to this     compressed spring, on a smooth, horizontal surface, and then released?

22. A 4.0 kg cart moving at 5.0 m/s[R] collides head-on with a 2.0 kg cart moving at 4.0 m/s[L]. Their collision is cushioned by a linear elastic spring between them.

a.  What is the total energy of the system before the collision?

b.  At minimum separation, what is the velocity of each cart? (Hint: @ min. sep. v1' = v2' = vmin  )

c.   Calculate the total kinetic energy at minimum separation.

d.   If the force constant of the spring is 900 N/m, what is its maximum compression during the collision?

23. A bullet’s speed may be determined by firing it into a sandbag pendulum, and measuring the vertical height to which the pendulum rises, as shown. (The bullet stays in the           sandbag.)

a.  What is the change in gravitational potential energy of the sandbag and bullet during the swing?

b.  What is the velocity of the sandbag-bullet combination at the start of the swing?

c.   What is the original velocity of the bullet?

d.   Explain why the collision between the bullet and the sandbag is inelastic?

24. Determine the momentum of the following objects:

a.   an electron of mass 9.11 × 10-31 kg travelling north at 6.45 × 106  m/s

b.   a 4.0 × 105  kg jet travelling south at 755 km/h

25. What impulse is exerted in each case?

a.   a force of 35 N[W] on a dynamics cart for 2.3 s

b.  the Earth pulling down on a 16 kg rock during the 4.0 s it takes to fall from a cliff

26. A student practises his batting at a local batting cage.

a.  A 0.350 kg baseball is travelling at 46 m/s toward the batter. After the batter hits the ball, the ball is travelling at 62 m/s in the opposite direction. What is the        impulse of the interaction?

b.   If the duration of the interaction is 25 ms, what is the average force exerted on the ball by the batter?

27. A 80 kg girl running at 3.5 m/s jumps onto a sled that has a mass of 10 kg and that is moving in the opposite direction to the girl, at 2.0 m/s. What will be the final velocity of the girl and the sled, assuming that she manages to hang on, that the sled is on level snow and that there is no friction?

28. A 125 kg astronaut pushes off from his 2500 kg space capsule, quickly acquiring a       constant velocity of 4.0 m/s. (Assume that both the astronaut and spacecraft are at rest to begin with.)

a.  What is the velocity of the space capsule, after he pushes off?

b.   If he is tethered to the space capsule by a 20 m line, what time will elapse before the line becomes taut? (Hint: think relative velocities!)

29. Two charged spheres, 3.0 cm apart, repel each other with a force of 2.4 x 10-8  N.            Determine the magnitude and sign of the charge on each, if one has twice the charge (of the same sign) as the other.

30.

31. Charged spheres A and B are fixed in position, as shown, and have charges of +4.0 µC  and -2.5 µC, respectively. Calculate the net force on sphere C, whose charge is +6.4 µC.

32. Two neutral spheres are attached to two identical springs and separated by 8.0 cm as    shown. When a charge of 2.5 x 10-6 C is placed on each sphere, the distance between   the spheres doubles. Calculate the force constant “k” of the springs. Be sure to include a FBD of one of the spheres! (Hint: FE  = FQ)

33.

34. Two identical metal spheres, each with positive charge “q” , are separated by a              centre-to-centre distance “r” . What effect will each of the following changes have on the magnitude of the electric force “F” exerted on each sphere by the other? Express your  answer as a multiplier.

a.  The distance between the two spheres is doubled.

b.  The distance between the two spheres is decreased to 1/3.

c.   Both charges are tripled.

d.   One of the charges becomes negative.

e.   One sphere is touched by identical neutral sphere, which is then taken far away and the distance is decreased to 2/5.

35. A positive charge of +3.2 x 10-6 C experiences an electric force of magnitude 4.0 N,    acting to the left. What is the magnitude and direction of the electric field at that point?

36. Calculate the electric field intensity midway between two negative charges of 4.3 x 10-9 C and 8.6 x 10-9 C that are 20 cm apart. Include a diagram of the situation.

37. Two 2.0 g spheres are attached to each end of a silk thread 1.20 m long. The spheres are given identical charges and the midpoint of the thread is then suspended from a   point on the ceiling. The spheres come to rest in equilibrium, with their centres 15 cm apart.

a.   Draw a diagram of the situation.

b.   Draw a FBD of one of the spheres.

c.   What is the magnitude of the charge on each sphere?

38. Two small oppositely charged spheres X and Y are fixed in position, as shown, and have charges of +40 µC and -40 µC, respectively. Determine the magnitude and direction of   the net electrical field (Enet) at point Z in the diagram given, due to the charges at points  X and Y. (Hint: Z is a small positive test charge!)

39.