practise mechanics

8/11/2019 Practise Mechanics

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Physics Mechanics Revision Planner Name:___________

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Week 8



NCEA 2003 QUESTION ONE: Practice Run

Andrew is racing a car at the speedway. He drives the car in a clockwise direction, as shown in thediagram below. The length of the track is 790 m.

(a) During a practice run, Andrew takes 25 seconds to complete one lap. Calculate the averagespeed of the car.

Average speed =

(b) The car is moving along a straight section of the track at a speed of 26 m s –1. The combinedmass of Andrew and his car is 1200 kg.

Calculate the kinetic energy of Andrew and his car.

Kinetic energy =

Andrew now accelerates the car at 1.2 m s –2 for 7.2 seconds.

(c) Calculate the speed of the car at the end of this 7.2 second period.

Speed =

(d) Calculate the distance that the car travels during this 7.2 second period

Distance =



Towards the end of the practice run, the car is moving along a straight section at a constant speed of 12 ms –1 for 8.0 seconds. The driving force required to keep the car moving at this constant speed is 400 N.

(e) Calculate the power produced by the engine to keep the car moving at this constant speed.Give a unit with your answer.

Power = (unit)

(f) Even though energy is being supplied to the car, the kinetic energy of the car is not increasing.Explain what happens to the energy.

NCEA 2003 QUESTION TWO: Getting Around Corners

The curved ends of the track are semicircles of radius 56 m. The car is now travelling along thesemicircular part of the track at a constant speed as shown below. It takes 6.77 seconds to complete one

of the semicircular parts of the track. (The length of a semicircle is pr.)

(a) Show that the speed of the car is 26 m s –1

(b) The combined mass of Andrew and the car is 1200 kg.

Calculate the size of the force acting on the car at the position shown in the diagram above.

Force =



(c) On the diagram above, draw an arrow to show the direction of the force acting on the car. Labelthis arrow ‘F’.

(d) Explain why circular motion at a constant speed needs a force.

Andrew is now at the other end of the track, where he drives over a large slippery oily patch.

(e) Describe what you would expect to happen to the speed and the direction of the car.

(f) Explain why this happens to the speed and the direction of the car.

NCEA 2003 QUESTION THREE: Andrew’s Mistake

When Andrew drives around a corner towards the end of the race, the car skids and collides into the safetybarrier. Before the collision, the car was travelling left at 18 m s –1. After the collision, it was travelling at 12m s –1 at right angles to its original motion, as shown below.

(g) On the grid below, and using the scale provided, draw vectors to show:

(i) the velocity of the car before the collision

(ii) the velocity of the car after the collision.

(h) On the grid below, draw a vector diagram to show the change in velocity of the car.



Scale: 1 square = 2 m s –1

Use your vector diagram to calculate the size and the direction (measured from the finalvelocity vector) of the change in velocity of the car.

(i) Speed =

(ii) Direction =

A few moments after the collision, the car is towed away by a tractor, as shown in the diagram below.

(i) Draw arrows on the diagram to show the horizontal forces acting on the car as it is being towedaway. Label the forces.

(j) When the tractor begins to pull the car, the tow rope stretches. The spring constant o f the towrope is 29 500 N m –1. The tow rope stretches 0.085 m when the car begins to move.

Calculate the force needed to start moving the car.

Give your answer to the correct number of significant figures.

Force =

(k) On one occasion, the tractor pulls the car with a force of 1650 N and the car accelerates at aconstant rate of 1.1 m s –2 for a distance of 36 m. (The combined mass of Andrew and the car is1200 kg.)

Calculate the work done against the friction.

Work =



NCEA 2003 QUESTION FOUR: Collision

During a later race, two cars travelling in the same direction collide. The diagram below shows the positionsof the cars before the collision. Car B has a mass of 1200 kg and is travelling at 28 m s –1.

(l) Show that the momentum of car B before the collision is 33 600 kg m s

(b) Car A has a mass of 1400 kg and is travelling at 21 m s –1.

Calculate the size of the total momentum of the cars before the collision.

Momentum =

Car B collides into the back of car A. After the collision, both cars are still travelling in the same direction.The momentum of car B after the collision is 26 000 kg m s –1.

(c) Calculate the velocity of car B just after the collision.

Velocity =

(d) Explain why the total momentum of the cars remains constant during the collision.

(e) Calculate the size of the change in momentum of car B and state its direction.

Size = Direction =

(f) The cars were in contact for 1.3 seconds. Calculate the average force during the collision.

Average force =



NCEA 2004 QUESTION ONE: SCHOOL SPORTS – RUNNING

Ana runs a 400 m race around the school track in 65 seconds.

(a) Calculate Ana’s average speed for the race.

Average speed =

(b) At the start of the race, Ana accelerates to a speed of 6.0 ms –1 during the first 2.2 seconds. Calculate

her acceleration, assuming it is constant.

Acceleration =

(c) Calculate the distance that Ana travels during these first 2.2 seconds.

Distance =



(d) During the middle part of the race, Ana, whose mass is 55 kg, is running at a steady speed of 6.5 m

s –1. Calculate her kinetic energy at this point in the race. State the unit for your answer.

Kinetic energy = (unit) .

(e) At the end of sports day, Ana drives home. During part of her journey, her car travels horizontally

along a straight road for 40 m at a constant speed of 15 m s –1. At this speed the car engine produces

6000 W of power. Calculate the size of the force needed to keep the car moving at this speed.

Force =

NCEA 2004 QUESTION TWO: SCHOOL SPORTS – JAVELIN

Where needed, use g = 10.0 m s –2.

Joe is taking part in a javelin competition. The javelin behaves like a projectile.

(a) Name the shape of the path of the javelin.



(b) Ignoring air resistance, draw arrow(s) on the drawing of the javelin below to show the force(s) acting

on it when it is in the position shown. Name the forces.

Joe now throws the javelin into the air at an angle of 40° above the horizontal at an initial velocity of

30 m s –1.

(c) Show that the horizontal component of the initial velocity of the javelin is 23 m s –1.

(d) Calculate the range (horizontal distance travelled) of the javelin under these conditions.

Range =



NCEA 2004 QUESTION THREE: SCHOOL GYM

Where needed, use g = 10.0 m s –2.

(a) The Trampoline

Henry is bouncing on the elastic mat of a trampoline.

In order to gain the necessary height to perform a certain move, Henry has stretched the mat

downwards by 0.50 m. The spring constant of the mat is 3500 N m –1.

(i) Calculate the size of the force supplied by the mat when stretched by this amount.

Force =

(ii) On the diagram below, draw labelled arrow(s) to show the force(s) acting on Henry when he is

at the lowest point of his bounce.



Henry has a mass of 75 kg.

(iii) Calculate the value of the net force acting on Henry when the trampoline mat is stretched

downwards by 0.50 m.

Net force =

(iv) State the direction of this net force.

(v) Calculate Henry’s initial acceleration when the mat is stretched downwards by 0.50 m.

Acceleration =

(vi) Calculate the vertical height to which Henry will rise above his lowest position.

Height =

(vii) Explain the physics involved in finding the answer to (vi), including a statement of any

assumptions made.



(b) The Balance Beam

Nadia is performing an exercise on the balance beam. The beam is 5.00 m long and has two

supports, A and B, each 0.50 m from either end. The beam is uniform and rigid and has a mass of 90

kg. Nadia’s mass is 55 kg and she is standing 1.50 m from the left hand end as shown below.

(i) On the diagram, draw four labelled arrows in the correct positions and pointing in the correct

directions to show each of the following forces

(1) Nadia’s weight

(2) The weight of the beam

(3) The support force provided by support A

(4) The support force provided by support B

(ii) State the value of

(1) Nadia’s weight

(2) The weight of the beam

(1)

(2)

(iii) Calculate the value of the support force at A when Nadia is in the position shown.

Force =

(iv) Explain the physics involved in finding the answer to (iii).



NCEA 2004 QUESTION FOUR: SCHOOL TRIP – ICE SKATING

Ana is warming up on the ice. She skates in a straight line at a speed of 10 m s –1 and then she changes her

speed to skate at a speed of 6.0 m s –1 at right angles to her original direction, as shown in the diagram

below.

vbefore = 10 m s –1

vafter = 6.0 m s –1

(a) On the grid below, and using the scale given, draw labelled arrows to show

(i) Ana’s initial velocity

(ii) Ana’s final velocity




(b) On the grid below, draw a vector diagram to show the change in Ana’s velocity.


Use your vector diagram to calculate the size and the direction of the change in Ana’s velocity. Showclearly on your diagram which angle you have calculated.

(i) Speed =

(ii) Direction =

Ana and Jon are now practising ice skating routines. Jon (mass 75 kg) skates at 6.0 m s –1 towards Ana

(mass 55 kg) who is standing still on the frictionless ice. Jon collides with Ana and they move off together in

the same straight line that Jon was moving before the collision.

(c) Calculate the speed of the skaters after the collision.

Speed =

(d) Explain the physics involved in finding the answer to (c), including a statement of any assumption

made.



In another skating move, Jon spins Ana around in a horizontal circle.

You may assume that Ana moves in a circle as shown below.

(e) Draw an arrow on the diagram to show the direction of the tension force that Jon’s arm exerts on Ana

at the instant shown.

(f) If the radius of the circle is 0.95 m and the tension force in Jon’s arm is 5.00 x 102 N, calculate the

speed with which Ana is travelling around the circle. Give your answer to the correct number of

significant figures.

Speed =

(g) While Ana is still moving in a circle on the ice, Jon lets her go.

(i) Describe her velocity (speed and direction) after he releases her.

(ii) Explain why Ana travels with this velocity.



NCEA 2005 QUESTION ONE: TRAVELLING BY CAR

(a) A car starts from rest at traffic lights and accelerates in a straight line to a speed of 50.0 km h – 1 in 10

seconds.

Using the approximation that 50.0 km h – 1 = 13.9 m s – 1, show that the car’s acceleration is

1.4 m s – 2.

(b) The mass of the car and its occupants is 1357 kg. Calculate the net force acting on the car when it is

accelerating.

(c) State whether the force that you calculated in your answer to (b) is equal to, less than or greater than

the total driving force provided by the car’s engine.

(d) Explain clearly the reason for your answer to part (c).

(e) Calculate the car’s power output during the first 10 seconds of its motion. Give the correct unit for

your answer.

(unit)

(f) Some time later the car is travelling in an easterly direction with an initial velocity of 12 m s – 1. It

makes a right hand turn, and then travels south with a final velocity of 16 m s – 1.



(i) On the grid below, using a scale of 1 cm = 2 m s – 1, draw labelled vectors to represent the initial

and final velocities of the car.

(ii) On the grid below, using a scale of 1 cm = 2 m s – 1, draw a labelled vector diagram showing the

change in velocity of the car.

An extra copy of the grid is reproduced at the end of the examination paper in case you

need to redraw your diagram. Ensure that you cross out work that is not to be marked.



(iii) Calculate the size of the change in velocity of the car.

(iv) Calculate the direction of the change in velocity of the car.

(g) The car is now travelling on the open road at a constant speed of 25 m s – 1. Part of the road forms the

arc of a circle of radius 40 m. The mass of the car and its occupants is still 1357 kg.

(i) On the diagram above, use a labelled arrow to show the direction of the resultant force acting on

the car as it travels around the corner at constant speed.

(ii) Calculate the value of this force. Give your answer to the correct number of significant figures.

(iii) Explain clearly, with reasons, what would happen to the car if the road was icy and could not

provide any of the force calculated in (ii).

(h) One of the reasons why cars have suspension systems is to help provide a smooth ride. Part of thesuspension system consists of four springs, one at each corner of the car.

(i) The spring constant of each of the car’s springs is 2.26 104 N m – 1. Assuming that the weight

of the occupants is evenly shared between the four springs, calculate how much the car sinks

down when the driver and passengers (total mass 357 kg) all get into the car.

(ii) Calculate how much energy is stored in one front spring if it is compressed by 0.12 m.



NCEA 2005 QUESTION TWO: A COLLISION

A car and its driver have a combined mass of 1200 kg. The car collided with a stationary van of mass 1500

kg. The car and van locked together after impact and from the marks on the road the police were able to

deduce that the wreckage moved at 4.0 m s – 1 immediately after the collision.

(a) Calculate the speed of the car just before it collided with the van.

(b) State what physical quantity is conserved in the collision.

(c) State the condition necessary for the quantity you have named in (b) to be conserved.

(d) The impact lasted for 0.50 seconds. Calculate the average force that the car exerted on the van during

the collision.

(e) Explain TWO features that a car has in order to reduce injury to the driver during a collision.

(f) Use calculations to explain whether the collision was elastic or inelastic.



NCEA 2005 QUESTION THREE: TRAVELLING IN A HOT AIR BALLOON

A hot air balloon is rising vertically at a constant speed of 2.5 m s – 1.

(a) Compare the sizes of the total upward force acting on the hot air balloon with the total downward

force acting on it, giving your reasons.



Some time later, the hot air balloon is hovering in a stationary position, 320 m above the sea. One of the

passengers throws a tennis ball with a speed of 25 m s – 1 in a horizontal direction as shown in the diagram

below.

(b) Assuming that it was a calm day with no wind, calculate the horizontal distance d from the balloon to

where the ball lands in the sea.

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