mechanics worksheet 1

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   T     h   e  G   a     l   a   x   y  S   c     h   o   o     l Mechanics Worksheet-1 Dr. Chirag Jhala The Galaxy School March 25, 2014 Submission: 28/03/2014 Name : Page: 1 2 3 4 5 6 7 8 9 10 11 12 Total Points: 2 2 1 2 2 2 1 2 4 3 3 1 25 Score: 1. [1] The graph shows the variation with time t of the velocity v  of an object. Which one of the following graphs best represents the variation with time  t  of the acceleration a of the object? A B C D  A    B    C    D 2. [1] A ball, initially at rest, takes time t  to fall through a vertical distance  h. If air resistance is ignored, the time taken for the ball to fall from rest through a vertical distance 9h  is  3t.    5t.    9t.    10t.

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    MechanicsWorksheet-1

    Dr. Chirag JhalaThe Galaxy School

    March 25, 2014Submission: 28/03/2014

    Name :

    Page: 1 2 3 4 5 6 7 8 9 10 11 12 Total

    Points: 2 2 1 2 2 2 1 2 4 3 3 1 25

    Score:

    1. [1]The graph shows the variation with time t of the velocity v of an object.

    Which one of the following graphs best represents the variation with time t of the acceleration a ofthe object?

    A B

    C D

    A B C D2. [1]A ball, initially at rest, takes time t to fall through a vertical distance h. If air resistance is ignored,

    the time taken for the ball to fall from rest through a vertical distance 9h is

    3t. 5t. 9t. 10t.

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    3. [1]The diagram below shows the path of a projectile in the absence of air resistance.

    Which one of the following diagrams best represents the path of the projectile under the same initialconditions when the air resistance is taken into account? (The path in absence of air resistance isshown for comparison as a dotted line.)

    A B

    C D

    A B C D4. [1]A sailing boat is moving with constant velocity v to the right parallel to the dock.

    Sailor Hulot, up on the mast, drops his telescope at the moment he is opposite Lucie who is standing

    on the dock. Which one of the following best shows the path of the falling telescope as seen byLucie?

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    A B

    C D

    A B C D

    5. [1]An athlete runs round a circular track at constant speed. Which oneof the following graphs bestrepresents the variation with time t of the magnitude d of the displacement of the athlete fromthe starting position during one lap of the track?

    A B

    C D

    A B C D

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    6. [1]A ball is dropped from rest at time t = 0 on to a horizontal surface from which it rebounds. Thegraph shows the variation of time t with speed v of the ball.

    Which one of the following best represents the point at which the ball just loses contact with thesurface after the first bounce?

    A B C D

    7. [1]A car accelerates uniformly from rest. It then continues at constant speed before the brakes areapplied, bringing the car to rest. Which of the following graphs best shows the variation with time

    t of the accelerationa of the car?

    A B

    C D

    A B C D

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    8. [1]Juan is standing on the platform at a railway station. A train passes through the station with speed20 m/s in the direction shown measured relative to the platform. Carmen is walking along one ofthe carriages of the train with a speed of 2.0 m/s measured relative to the carriage in the directionshown. Velocity is measured as positive in the direction shown on the diagram.

    The velocity of Carmen relative to Juan is

    -22 m/s. -18 m/s. +18 m/s. +22 m/s.9. [1]A stone is thrown with speed v from the top of a cliff of height H, as shown below.

    The stone is thrown at an angle to the horizontal so that it rises to a height h above the top of thecliff before falling into the sea. The acceleration of free fall is g. Air resistance is negligible. Whichone of the following expressions gives correctly the speed of the stone as it hits the sea?

    v + 2gh v +2gH

    2g(h+H)

    v2 + 2gH

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    10. [1]A block rests on a rough surface. Two forces P and Q act on the block, parallel to the surface.A friction force F between the block and the surface keeps the block in equilibrium. Which vectordiagram best represents the three forces?

    A B

    C D

    A

    B

    C

    D

    11. [1]A bird of weight W lands at the midpoint of a horizontal wire stretched between two poles. Themagnitude of the force exerted by each pole on the wire is F.

    The bird will be in equilibrium if

    2F W. 2F = W. 2F W. F = W.

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    12. [1]A small electrically charged sphere is suspended vertically from a thread. An oppositely charged rodis brought close to the sphere such that the sphere is in equilibrium when displaced from the verticalby an angle of 45.

    Which one of the following best represents the free body diagram for the sphere?

    A B

    C D

    A B C D

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    13. [1]An object on the end of a light flexible string rotates in a circle as shown below.

    The tension in the string is T when the string is at angle to the vertical. Which of the followingis true?

    State Resultant forceA not in equilibrium TB not in equilibrium T sin()C in equilibrium TD in equilibrium T sin()

    A B C D14. [1]14. A light inextensible string has a mass attached to each end and passes over a frictionless pulley

    as shown.

    The masses are of magnitudes M and m, where m M. The acceleration of free fall is g. Thedownward acceleration of the mass M is

    MmM+m

    g Mm

    M

    g

    M+mMm

    g

    M

    M+m

    g

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    15. [1]The engine of a rocket ejects gas at high speed, as shown below.

    The rocket accelerates forwards because

    the momentum of the gas is equal but opposite in direction to the momentum of the rocket. the gas pushes on the air at the back of the rocket.

    the change in momentum of the gas gives rise to a force on the rocket. the ejected gas creates a region of high pressure behind the rocket.16. [1]Three forces of magnitude F1 = 3.0 N, F2 = 4.0 N and F3 = 6.0 N act at a point.The point is in

    equilibrium. The magnitude of the resultant ofF1 and F2 is

    1.0 N. 5.0 N. 6.0 N. 7.0 N.17. [1]A toy cannon is mounted vertically on a cart. The cart is moving along a straight-line with constant

    speed. A spring inside the cannon shoots a ball vertically upwards.

    No resistance forces act on the cart and on the ball. Which one of the following statements is true

    about the position where the ball will land? The position depends on the speed of the cart. The ball will land inside the cannon. The ball will land behind the cannon. The ball will land in front of the cannon.

    18. [1]A general expression for Newtons second law of motion is F = Pt

    . What condition is applied sothat the law may be expressed in the form ofF =m a?

    The mass m is constant. The acceleration a is constant.

    The force F is constant.

    The direction of the force F is constant.

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    19. [1]The diagram below shows five wooden blocks joined by inelastic strings. A constant force acceleratesthe blocks to the right on a frictionless horizontal table.

    In which string is the tension the greatest?

    W X Y Z20. [1]Sand falls vertically on a conveyor belt at a rate ofm kg /s.

    In order to keep the belt moving at constant speed v the horizontal force that must be exerted onthe belt is

    m v. 12

    m v. m v2. 12

    m v2.

    21. [1]A stone of mass m is attached to a string. The stone is made to rotate in a vertical circle of radiusr, as shown.

    At the point where the stone is vertically above the centre of the circle, the stone has speed v. Whichof the following expressions gives the tension in the string?

    m g - mv2r

    . mv2r

    . mv2r

    - m g . mv2r

    + m g .

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    22. [1]A trolley of mass 1.5 kg is pulled along a horizontal table by a force of 5.0 N.

    The frictional force acting on the trolley is 0.50 N. The acceleration of the trolley is

    0.30 m/s2. 0.33 m/s2. 3.00 m/s2. 3.30 m/s2.23. [1]In a fairground ride, a car of mass M travels on rails around a vertical loop of effective radius R.

    At the top of the loop, the speed of the car is v. The car stays in contact with the rails, as shownbelow.

    Which of the following is the correct expression for the force that the rails exert on the car?

    M v2R

    - M g. Mv2R

    . M g . Mv2R

    +M g.

    24. [1]A sphere of mass m strikes a vertical wall and bounces off it, as shown below.

    The magnitude of the momentum of the sphere just before impact is pB and just after impact is pA.The sphere is in contact with the wall for time t. The magnitude of the average force exerted by thewall on the sphere is

    pBpAt pB+pA

    t pBpA

    m t pB+pA

    mt

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    25. [1]A brick is placed on the surface of a flat horizontal disc as shown in the diagram below. The disc isrotating at constant speed about a vertical axis through its centre. The brick does not move relativeto the disc.

    Which of the diagrams below correctly represents the horizontal force or forces acting on the brick?

    A B

    C D

    A B C D

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