1. This question is about the kinematics of an elevator (lift).
(a) Explain the difference between the gravitational mass and the inertial mass of an object.
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(3)
An elevator (lift) starts from rest on the ground floor and comes to rest at a higher floor. Its motion is controlled by an electric motor. A simplified graph of the variation of the elevator’s velocity with time is shown below.
0 . 8 0 0 . 7 0 0 . 6 0 0 . 5 0 0 . 4 0 0 . 3 0 0 . 2 0 0 . 1 0 0 . 0 0
0 . 0 1 . 0 2 . 0 3 . 0 4 . 0 5 . 0 6 . 0 7 . 0 8 . 0 9 . 0 1 0 . 0 1 1 . 0 1 2 . 0 t i m e / s v e l o c i t y / m s – 1
(b) The mass of the elevator is 250 kg. Use this information to calculate
(i) the acceleration of the elevator during the first 0.50 s.
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(2)
(iii) the minimum work required to raise the elevator to the higher floor.
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(2)
(iv) the minimum average power required to raise the elevator to the higher floor.
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(2)
(v) the efficiency of the electric motor that lifts the elevator, given that the input power
to the motor is 5.0 kW.
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(2)
(c) On the graph axes below, sketch a realistic variation of velocity for the elevator. Explain
your reasoning. (The simplified version is shown as a dotted line)
0 . 8 0 0 . 7 0 0 . 6 0 0 . 5 0 0 . 4 0 0 . 3 0 0 . 2 0 0 . 1 0 0 . 0 0
0 . 0 1 . 0 2 . 0 3 . 0 4 . 0 5 . 0 6 . 0 7 . 0 8 . 0 9 . 0 1 0 . 0 1 1 . 0 1 2 . 0 t i m e / s v e l o c i t y / m s – 1
The elevator is supported by a cable. The diagram below is a free-body force diagram for when the elevator is moving upwards during the first 0.50 s.
t e n s i o n
w e i g h t
(d) In the space below, draw free-body force diagrams for the elevator during the following
time intervals.
(i) 0.5 to 11.50 s (ii) 11.50 to 12.00 s
(3)
A person is standing on weighing scales in the elevator. Before the elevator rises, the reading on
the scales is W.
(e) On the axes below, sketch a graph to show how the reading on the scales varies during the
whole 12.00 s upward journey of the elevator. (Note that this is a sketch graph – you do
not need to add any values.)
r e a d i n g o n s c a l e s
(f) The elevator now returns to the ground floor where it comes to rest. Describe and explain the energy changes that take place during the whole up and down journey.
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(4) (Total 25 marks)
2. This question is about projectile motion.
A marble is projected horizontally from the edge of a wall 1.8 m high with an initial speed V.
g r o u n d 1 . 8 m
A series of flash photographs are taken of the marble. The photographs are combined into a single photograph as shown below. The images of the marble are superimposed on a grid that
shows the horizontal distance x and vertical distance y travelled by the marble.
The time interval between each image of the marble is 0.10 s.
0
– 0 . 5 0
– 1 . 0
– 1 . 5
– 2 . 0
0 0 . 5 0 1 . 0 1 . 5 2 . 0
x / m
y / m
(a) On the images of the marble at x = 0.50 m and x = 1.0 m, draw arrows to represent the
horizontal velocity VH and vertical velocity VV.
(2)
(b) On the photograph, draw a suitable line to determine the horizontal distance d from the
base of the wall to the point where the marble hits the ground. Explain your reasoning. ... ... ...
(3)
(c) Use data from the photograph to calculate a value of the acceleration of free fall.
3. This question is about linear motion.
A police car Pis stationary by the side of a road. A car S, exceeding the speed limit, passes the
police car P at a constant speed of 18 m s–1. The police car P sets off to catch car S just as car S
passes the police car P. CarPaccelerates at 4.5 m s–2 for a time of 6.0 s and then continues at
constant speed. Car Ptakes a time t seconds to draw level with car S.
(a) (i) State an expression, in terms of t, for the distance car S travels in t seconds.
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(1)
(ii) Calculate the distance travelled by the police carPduring the first 6.0 seconds of its
motion.
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(1)
(iii) Calculate the speed of the police carPafter it has completed its acceleration.
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(1)
(iv) State an expression, in terms of t, for the distance travelled by the police car P
during the time that it is travelling at constant speed.
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(1)
(b) Using your answers to (a), determine the total time t taken for the police car Pto draw
level with car S.
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4. Linear motion
At a sports event, a skier descends a slope AB. At B there is a dip BC of width 12 m. The slope and 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 m
d i p 1 2 m
The graph below shows the variation with time t of the speed v down the slope of the skier.
2 5 . 0
2 0 . 0
1 5 . 0
1 0 . 0
5 . 0
0 . 0
8 . 0 7 . 0 6 . 0 5 . 0 4 . 0 3 . 0 2 . 0 1 . 0 0 . 0
v / m s– 1
t / s
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
(ii) determine the length of the slope.
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(4)
(b) (i) Calculate the change EP in the gravitational potential energy of the skier between
point A and point B.
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(2)
(ii) Use your answers to (a) and (b)(i) to determine the average retarding force on the
skier between point A and point B.
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(3)
(iii) Suggest two causes of the retarding force calculated in (ii).
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(2)
(c) At point B of the slope, the skier leaves the ground. He “flies” across the dip and lands on
the lower side at point D. The lower side C of the dip is 1.8 m below the upper side B. Determine the distance CD of the point D from the edge C of the dip. Air resistance may be assumed to be negligible.
(d) The lower side of the dip is altered so that it is inclined to the horizontal, as shown below.
s l o p e B C D
d i p
1 2 m
1 . 8 m
(i) State the effect of this change on the landing position D.
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(1)
(ii) Suggest the effect of this change on the impact felt by the skier on landing.
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