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8/3/2019 PRUEBA_DE_MECANICA

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Prueba de FsicaSegundo de Bachillerato C

Nombre:_________________________________ Fecha: ____ / ____ / ____Puntos: ____ / 20

1. A mass is suspended from the roof of a lift (elevator) by means of a spring balance, asillustrated below.

l i f t ( e

m a s s

The lift (elevator) is moving upwards and the readings of the spring balance are noted asfollows.

Accelerating: Ra

Constant speed: Rc

Slowing down: Rs

Which one of the following is a correct relationship between the readings?

A. Ra >Rc B. Ra =Rs

C. Rc =Rs D. Rc


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Total linear momentum of the bodies Total kinetic energy of the bodies

A. Yes Yes

B. Yes No

C. No Yes

D. No No

(1)

4. A sphere of mass m strikes a vertical wall and bounces off it, as shown below.

m o m e n t u mp

m o m e n t u mp

B

A

w

The magnitude of the momentum of the sphere just before impact ispBand just after impact is

pA.The sphere is in contact with the wall for time t. The magnitude of the average force exerted

by the wall on the sphere is

A.

( )

t

ppAB

. B.

( )

t

ppAB

+

.

C.

( )

mt

pp AB

. D.

( )

mt

pp AB +

.(1)

5. An object of mass m1has a kinetic energyK1. Another object of mass m2has a kinetic energy

K2.If the momentum of both objects is the same, the ratio 2

1

K

K

is equal to

A. 1

2

m

m

. B. 2

1

m

m

.

C. 1

2

m

m

. D. 2

1

m

m

.(1)


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6. The graph below shows the variation with displacement dof the forceFapplied by a spring ona cart.

5

4

3

2

1

00 1 2 3

d / 1 0 2

F N/

The work done by the force in moving the cart through a distance of 2 cm is

A. 10 102

J. B. 7 102

J.

C. 5 102

J. D. 2.5 102

J.(1)

7. Linear motion

At a sports event, a skier descends a slope AB. At B there is a dip BC of width 12 m. The slopeand dip are shown in the diagram below. The vertical height of the slope is 41 m.

A

B C D

4 1 m

s l o p e

( n o t t o s c a l e )

1 . 8

d i p 1 2 m

The graph below shows the variation with time tof the speed v down the slope of the skier.

2 5 . 0

2 0 . 0

1 5 . 0

1 0 . 0

5 . 0

0 . 08 .7 . 06 . 05 . 04 . 03 . 02 . 01 . 00 . 0

v / m s 1

t / s


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The skier, of mass 72 kg, takes 8.0 s to ski, from rest, down the length AB of the slope.

(a) Use the graph to

(i) calculate the kinetic energyEKof the skier at point B.

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.........................................................................................................................(2)

(ii) determine the length of the slope.

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(b) (i) Calculate the magnitude of the change EP in the gravitational potential energy ofthe skier between point A and point B.

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.........................................................................................................................(2)

(ii) Use your anwers to (a)(i) and (b)(i) to determine the ratio

( ) .P

KP

EEE

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.........................................................................................................................(2)

(iii) Suggest what this ration represents.

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.........................................................................................................................(1)

(c) At point B of the slope, the skier leaves the ground. He flies across the dip and lands onthe lower side at point D. The lower side C of the dip is 1.8 m below the upper side B.

(i) Calculate the time taken for an object to fall, from rest, through a vertical distanceof 1.8 m. Assume negligible air resistance.

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......................................................................................................................... (2)


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(ii) The time calculated in (c)(i) is the time of flight of the skier across the dip.Determine the horizontal distance travelled by the skier during this time, assumingthat the skier has the constant speed at which he leaves the slope at B.

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.........................................................................................................................(2)

(Total 15 marks)

8. This question is about conservation of momentum and conservation of energy.

(a) State Newtons third law.

.....................................................................................................................................

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.....................................................................................................................................(1)

(b) State the law of conservation of momentum.

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.....................................................................................................................................(2)

The diagram below shows two identical balls A and B on a horizontal surface. Ball B is at rest

and ball A is moving with speed Valong a line joining the centres of the balls. The mass of eachball is M.

A B

v

B e f o r e c o l l i s i o n

During the collision of the balls, the magnitude of the force that ball A exerts on ball B isFABand the magnitude of the force that ball B exerts on ball A isFBA.

(c) On the diagram below, add labelled arrows to represent the magnitude and direction ofthe forcesFAB andFBA.

A BD u r i n g t h e c o l l i s i o n

(3)

The balls are in contact for a time t. After the collision, the speed of ball A is +vA and the

speed of ball B is +vB in the directions shown.


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A BA f t e r t h e c o l l i s i o n

v A v B

As a result of the collision, there is a change in momentum of ball A and of ball B.

(d) Use Newtons second law of motion to deduce an expression relating the forces actingduring the collision to the change in momentum of

(i) ball B.

...........................................................................................................................

...........................................................................................................................(2)

(ii) ball A.

...........................................................................................................................

...........................................................................................................................(2)

(e) Apply Newtons third law and your answers to (d), to deduce that the change inmomentum of the system (ball A and ball B) as a result of this collision, is zero.

.....................................................................................................................................

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.....................................................................................................................................(4)

(f) Deduce, that if kinetic energy is conserved in the collision, then after the collision, ball Awill come to rest and ball B will move with speed V.

.....................................................................................................................................

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.....................................................................................................................................(3)

(Total 17 marks)

9. Mechanical power


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(a) A car drives up a straight incline that is 4.8 km long. The total height of the incline is 0.30km.

The car moves up the incline at a steady speed of 16 m s1

. During the climb, the average

friction force acting on the car is 5.0 102

N. The total weight of the car and the driver is

1.2 104

N.

(i) Determine the time it takes the car to travel from the bottom to the top of theincline.

.........................................................................................................................

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.........................................................................................................................(2)

(ii) Detemine the work done against the gravitational force in travelling from thebottom to the top of the incline.

.........................................................................................................................(1)

(iii) Using your answers to (a)(i) and (a)(ii), calculate a value for the minimum poweroutput of the car engine needed to move the car from the bottom to the top of theincline.

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(b) From the top of the incline, the road continues downwards in a straight line. At the pointwhere the road starts to go downwards, the driver of the car in (a), stops the car to look atthe view. In continuing his journey, the driver decides to save fuel. He switches off the


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engine and allows the car to move freely down the hill. The car descends a height of 0.30km in a distance of 6.4 km before levelling out.

The average resistive force acting on the car is 5.0 102

N.

Estimate

(i) the acceleration of the car down the incline.

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.........................................................................................................................(5)

(ii) the speed of the car at the bottom of the incline.

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.........................................................................................................................(2)

(c) In fact, for the last few hundred metres of its journey down the hill, the car travels atconstant speed. State the value of the frictional force acting on the car whilst it is movingat constant speed.

...................................................................................................................................(1)

(Total 15 marks)

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