UNIT 1 - MOTION & ENERGY WORKSHEETS

NOTE: Material in this section of the website is being prepared based on the Draft Australian Physics Curriculum developed by ACARA (Australian Curriculum, Assessment and Reporting Authority).  The material itself and/or the arrangement of this material may change as the Australian Physics Curriculum reaches implementation stage in 2012-2013.

UNIT 1 - MOTION & ENERGY WORKSHEETS

VECTOR ANALYSIS WORKSHEET No.1

Answers are supplied.  Simply click on the word "answers" at the end of each question.

1.     A ship is heading due west at a steady speed of 15 km/h.  A current of 3 km/h is running due south.  Calculate the velocity of the ship relative to the seabed.  (Hint: The velocity of the ship plus the velocity of the current will add up to the total velocity of the ship relative to the seabed.)  Answers

2.     Two tractors pull on a large boulder in an effort to shift it out of the way of a new fence line.  One tractor pulls with a force of 3000 N west and the other tractor pulls with a force of 2500 N in a southerly direction because of the terrain.  Determine the resultant force acting on the boulder.  If the boulder has a mass of 1000 kg calculate the acceleration of the boulder due to the resultant force acting on it.  Answers

3.     Three coplanar horizontal forces each of magnitude 10 N act on a body of mass 5 kg as shown below.  Determine the magnitude of the net force acting on the body and the magnitude of the resultant acceleration.  Answers

4.     If vector A = 5 N north and vector B = 10 N east, find the resultant of vector A – vector B.  Answers

5.     A submarine is travelling at 20 km/h due east.  A short time later it is travelling due north at 15 km/h.  Calculate the change in velocity of the submarine.  Answers

6.     An F-117A Nighthawk stealth fighter jet has a true airspeed of  1000 km/h due east.  There is a cross wind blowing in a direction E60oS at 100 km/h.  Calculate the velocity of the jet relative to the ground.  (Hint: You will need to use the cosine & sine rules if you intend to do this question mathematically.)  Answers

7.      A sled of mass 10 kg sits on a horizontal surface as shown below.

A force is exerted on the sled by means of a rope inclined at 60o to the horizontal.  If the tension in the rope is 150 N and the frictional force between the sled and the horizontal surface is 55 N, will the sled move under these conditions?  Explain.  If the sled does move determine the size of the acceleration with which it moves.  Answers

8.     A barge of total mass 300 kg is pulled by a single rope attached to a tugboat of mass 1000 kg.  If the drag on the tug and the barge is one-tenth of their respective weights, and the total forward force exerted by the tug is 5130 kg force (ie 5130 x 9.8 N), find the magnitude of:

a.      the total force resisting the forward motion of the tug and barge;

b.      the acceleration of the tug/barge system;

c.       the unbalanced accelerating force on the barge;

d.      the tension in the towing rope.

9.     An astronaut of mass MA = 80 kg stands on the horizontal floor of a spaceship moving vertically with acceleration a.  If the acceleration due to gravity on the astronaut is g = 9.8 ms-2, write a mathematical expression for and calculate the value of the reaction force R between the astronaut and the floor of the spaceship when:

a.      a = 0;

b.      a = 8 ms-2 upwards;

c.       a = 8 ms-2 downwards.

ANSWERS TO VECTOR ANALYSIS WORKSHEET No.1

1.     15.3 km/h W11.3oS or S78.7oW

2.     Resultant force = 3905 N in a direction of W39.8oS & acceleration = 3.9 ms-2 in the same direction as the resultant force.

3.      Net force = 20 N & resultant acceleration = 4 ms-2.

4.      11.2 N in a direction of N63.4oW

5.      25 km/h in a direction of N53.1oW

6.      1054 km/h E5oS

7.     Horizontal force to the left on sled is 75 N, which is greater than the friction force to the right.  Therefore the sled will move to the left with an acceleration of 2 ms-2.  If you did not get the right acceleration, ask yourself how much of the 75 N to the left actually accelerates the sled – all of it or just some of it?  Some of it has to overcome friction!

8.      (a) 1274 N, (b) 37.7 ms-2, (c) 11 307 N, (d) 11 601 N.

9.      (a) R = MA g  = 784 N upwards; (b) R = MA g  + MA a = 1424 N upwards;  (c) R = MA g  - MA a = 144 N upwards.

FORCE – WORKSHEET 1

1.     Describe the typical effects of the following external forces acting on bodies:

a.      Friction between surfaces

b.      Air resistance

2.      In each of the following situations, forces act to cause a change in the velocity of a vehicle (car).  Outline (ie sketch in general terms; indicate the main features of) the forces involved:

a.      Coasting along a level road with no pressure on the accelerator

b.      Pressing on the accelerator

c.       Pressing on the brakes

d.      Passing over an icy patch on the road

e.      Climbing hills

f.        Descending hills

g.      Following a curve in the road

3.      Explain the difference between “mass” and “weight”.

4.      An unbalanced force of 48N west is applied to a 4 kg cart.  Calculate the cart’s acceleration.  (12ms-2 west)

5.      A 2200 kg car, travelling at 25 m/s south, comes to a stop in 10 s.  Calculate (a) the car’s acceleration and (b) the unbalanced force required to cause that acceleration.  (2.5 ms-2 north & 5500 N north)

6.      Astronauts are placed horizontally in their space capsule during launch.  Use Newton’s First Law to explain why this is a good idea.

7.      A particular pressure on the accelerator of a 4-wheel drive van of mass 2000 kg, travelling along a smooth, level road supplies sufficient force from the engine to accelerate the van at 5 ms-2.  When this same van travels through soft sand, the same pressure on the accelerator results in a constant velocity of the van.  Determine the force due to friction acting on the van in the soft sand.  (1 x 104N)

8.      The driver’s handbook in a particular country states that the minimum safe distance between vehicles on the road is the distance a vehicle can travel in 2 s at constant speed.  Assume that a 1200 kg car is travelling south at 72 km/h when the truck ahead crashes into a northbound truck and comes to a sudden stop.

a.      If the car is at the required safe distance behind the truck, what is the separation distance between the car and the truck in metres?  (40m)

b.      If the average braking force exerted by the car is 6400 N north, how long would it take the car to stop?  (3.75s)

c.       What additional data would you need to obtain to determine whether or not the car would be involved in a collision.  Assume that the car diver has a reaction time of 0.1s.

9.      The diagram below shows a spring balance connected via two inextensible strings to two identical masses.

What will be the reading (in newtons) on the spring balance?  Explain.

ENERGY - WORKSHEET 1

1.      A car is travelling at 27 m/s north and has a mass of 1500 kg.  Calculate the kinetic energy of the car.  (5.47 x 105 J)

2.      A 7500 kg truck travelling east at 5 ms-1 collides and coalesces with a 1500 kg car travelling south-west at 20 ms-1.  Describe the energy transformations that may occur during such a collision.

3.      Determine the amount of work that must be done by the engine of a 500 kg racing car to change the velocity of the car from 55 ms-1 east to 60 ms-1 east.  If this change in velocity was accomplished in 0.3 s, calculate the acceleration of the car.  Find the net force applied by the engine to cause this acceleration.  (143750 J, 16.67 ms-2, 8335 N)

4.      Determine the kinetic energy of a 300 kg space probe launched from the surface of Mars, once it has reached escape velocity of 5.1 km/s.  (3.90 x 109 J)

5.      An army tank of 2.5 x 104 kg mass has a kinetic energy of 1.25 x 106 J.  Calculate the speed of the tank.  (10ms-1)

MOMENTUM – WORKSHEET 1

1.      A 2200 kg car, travelling at 25 m/s south, comes to a stop in 10 s.  Calculate (a) the initial momentum of the car; (b) the final momentum of the car; (c) the impulse of the net force applied by the brakes; and (d) the magnitude of the net force applied by the brakes.  (55000 kgm/s south, 0 kgm/s, 55000 kgm/s north, 5500 N north)

2.      A hammer strikes a nail with a force of 55 N for a period of 0.2 s.  Calculate the impulse of the force.  (11 kgm/s)

3.      For how long must an explosive force of 3.3 x 104 N act on a stationary bullet of mass 0.15 kg to give it a velocity of 220 m/s?  (0.001 s)

4.      A mass of 4 kg experiences a varying force as given in the diagram below.  Determine the change in velocity of the mass.  (3 m/s)

MOMENTUM – WORKSHEET 2

1.      In experimental tests run by the manufacturer, a car of mass 1500 kg travelling at 20 ms-1 due east collides with an identical stationary car.  Assuming that all of the kinetic energy of the moving car is transferred to the stationary car during the collision, describe quantitatively and qualitatively the expected results of the collision.

2.      Laboratory Trolley Car A has a mass of 0.9 kg and Laboratory Trolley Car B a mass of 0.5 kg.  For each of the situations below, describe quantitatively and qualitatively the expected results of the collision for Car A:

a.      Car A moves east at 0.5 ms-1 and collides but does not coalesce with Car B moving west at the same speed.  After collision, Car B is moving east with a speed of 0.79 ms-1.  (Car A: v = 0.22 m/s west)

b.      Car A moves east at 0.5 ms-1 and collides but does not coalesce with Car B moving east at 0.3 ms-1.  After collision, Car B is moving east with a speed of 0.56 ms-1.  (Car A: v = 0.36 m/s east)

c.       Car A moves east at 0.4 ms-1 and collides but does not coalesce with Car B moving west at 0.3 ms-1.  After collision, Car B is moving east with a speed of 0.6 ms-1.  (Car A: v = 0.1 m/s west)

d.      Car A moving at 0.3 ms-1 east collides and coalesces with Car B moving at 0.5 ms-1 west.  (Car A & B: v = 0.014 m/s east)

(Hint: Use appropriate signs, +, -, to designate direction.)

3.      A car of mass 1300 kg travelling at 25 m/s south, collides with a solid rock cliff face.  Use your knowledge of force and momentum to describe a possible result of this collision.

4.      OPTIONAL: Go to the following URL and test out your answers to question 2 using the collision Java applet provided.  (This URL is a link on my Links page.)

REVISION WORKSHEET No.1

1.      Kate is chasing Angela with a large bucket of water.  She runs 100m due east, followed by 100m due north and then 150m due south.  Calculate Kate’s displacement from her start point at the end of her run.  Answers

2.      Brad’s Lamborghini has an initial velocity of 20ms-1 south and an acceleration of 5 ms-2 south for five seconds.  Determine:

a.      the total change in velocity of the car

b.      the final velocity of the car after five seconds.

3.      A car changes its velocity from 5 ms-1 south to 12 ms-1 east.  Calculate the change in velocity of the car.  Answers

4.      A car of mass 1000kg changes its velocity from 20ms-1 north to 30ms-1 north in 2 seconds.

a.      Determine the amount of work done by the engine of the car to achieve this change in velocity.

b.      Calculate the acceleration of the car and the net force applied by the engine to cause this acceleration.

5.      A truck of mass 5000kg travelling at 15ms-1 is brought to rest in a distance of 100m.

a.      Calculate the average force exerted by the truck’s brakes to achieve this change in velocity.

b.      Identify the energy transformations that occur as the truck’s kinetic energy is reduced to zero.

6.      A bus travels at constant speed of 12ms-1 around a circular bend of radius 150m.

a.      Determine the centripetal acceleration (magnitude & direction) of the bus as it negotiates the bend.

b.      Calculate the centripetal force acting on the bus (magnitude & direction), if the mass of the bus is 2000kg.

7.      A ship is heading due west at a steady speed of 15 km/h.  A current of 3 km/h is running due south.  Calculate the velocity of the ship relative to the seabed.  (Hint: The velocity of the ship plus the velocity of the current will add up to the total velocity of the ship relative to the seabed.)  Answers

8.      Two trucks pull on a large boulder in an effort to shift it out of the way of a new fence line.  One truck pulls with a force of 3000 N east and the other truck pulls with a force of 2500 N south-east.

a.      Determine the magnitude of the net force acting on the boulder.  (Hint: A scaled vector diagram would be helpful here.)

b.      If the boulder has a mass of 500 kg calculate the size of the acceleration of the boulder due to this net force.

9.      Two railway cars are being used in a structure integrity test.  Car A of mass 900 kg moves east at 25 ms-1 and collides but does not coalesce with Car B of mass 700kg moving west at 20 ms-1.  After collision Car B is moving east with a speed of 30.6 ms-1.  Determine:

a.      The total momentum of the system before collision.

b.      The total momentum of the system after collision.

c.       The speed and direction of Car A after collision.

d.      The change in momentum of Car A as a result of the collision.

e.      The average force acting on Car A, given that the change in momentum took 1.5 seconds.

10.  Study the graph below, which shows the velocity of a vehicle over a period of time.

Determine:

a.      The average speed of the vehicle from t = 2s to t = 4s.

b.      The instantaneous speed of the vehicle at t = 3s.

c.       The acceleration of the vehicle from t = 2s to t = 4s.

d.      The total distance covered from t = 0 to t = 4s.

1.      111.8m E26.6oS

2.      (a) 25ms-1 South; (b) 45ms-1 South

3.      13ms-1 E22.6oN

4.      (a) 2.5 x 105 J; (b) 5ms-2 north and 5000N north.

5.      (a) 5625N in opposite direction to original motion; (b) kinetic energy is transformed into sound & heat energy.

6.      (a) 0.96ms-2 towards centre of circular bend; (b) 1920N in same direction as the centripetal acceleration.

7.      15.3 km/h W11.3oS (or S78.7oW)

8.      (a) 5000N; (b) 10ms-2

9.      (a) 8500Ns East; (b) 8500Ns, East; (c) 14.35ms-1 West; (d) 35 415Ns, West; (e) 23 610N, West.

10.  (a) 2ms-1; (b) 1.8ms-1; (c) 2ms-2 in opposite direction to motion; (d) 12m.

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