Homework 1a : Significant Figures, Prefixes & Scientific Notation
1. In each of the following cases, the stated value has too many significant figures. The appropriate number of significant figures is stated in brackets after the quantity. Round each quantity to the correct number of significant figures.
(a) 11.85467 V (3 sig figs)
(b) 50.7835 Hz (2 sig figs)
(c) 0.000000712 m (3 sig figs)
(d) 2.998 x 108 ms-1 (2 sig figs) (2)
2. Calculate the following quantities from the information given, and report your answer to an appropriate number of significant figures. Remember to give your answer in scientific notation.
(a) Calculate the frequency of microwaves that have a wavelength of 3.1x10-2m. (1½)
(b)Calculate the energy used if a 1.2 kW kettle takes 2 minutes to boil water. (1½)
3. Copy the table below, and fill in all the blanks. (2)
Quantity / Value / Scientific NotationSpeed of light / 3x108ms-1
Charge on an electron / 0.000 000 000 000 000 000 160 C
Wavelength of red light / 7x10-7m
Voltage used in the Super Grid / 250 000 V
4. Re-write the following quantities using the most appropriate prefix. ( milli, kilo etc ) (3)
(a) 0.000 006 m
(b) 1 500 000 000 Hz
(c) 3200 W
(d) 0.008 g
(e) 2.7x106 J
(f) 7.42x10-7 m
Homework 1b - Uncertainties
(a) Give the ammeter and voltmeter readings and state the scale reading uncertainty in each case. (2)
(b) Use Ohm’s Law to calculate a value for the resistance. Estimate the absolute uncertainty in the calculated value of the resistance and explain how you arrived at your estimate. (3)
(c) The experiment is repeated 5 times, and the values recorded for the current are as follows:
0.44 A; 0.43 A; 0.45 A; 0.42 A; 0.44 A
Calculate the mean current, and the random uncertainty in the mean. (3)
2. A current is measured with an analogue meter which has scale divisions of 0.1 A, and is found to be 5.4A. The reading is double-checked with a digital meter, and again is found to be 5.4A. Using which instrument gives the larger scale reading uncertainty? Explain your answer. (2)
Homework 2 - Vectors
1. (a) Explain the difference between a vector and a scalar quantity. (1)
(b) Give 2 examples each of a vector and a scalar quantity.
2. A ferry crosses a river that is flowing at 5ms-1.
If the ferry is travelling at 12ms-1,
calculate its resultant velocity.
( 13ms-1,1130)
3. A boy using a force of 250 N pulls a sledge across the snow as shown in the diagram below. Calculate the horizontal and vertical components of this force. ( 192 and 161 N ) (2)
3. A footballer runs around a football pitch as part of his training. He starts at the halfway line (point X), and runs around the pitch to point D as shown. This run takes him 50 seconds.
(a) Calculate the total distance travelled by the footballer. (1)
(b) What is his final displacement at point D? (1)
(c) Calculate the footballer’s average velocity for the run. ( 1ms-1, 2700)
Homework 3 - Graphs
1) The velocity – time graph is shown below for an object moving over a 25 second time interval.
a) Describe the motion of the object from
1) 0 s – 5 s
2) 5 s – 15 s
3) 15 s – 18 s
4) 18 s – 25 s
b) Calculate the total displacement of the object. ( 122.5m )
c) Calculate the magnitude of average velocity over the 25 second time interval. ( 4.9 ms-1 )
d) Draw the corresponding acceleration - time graph for the 25 second time interval on a piece of graph paper.
2) The acceleration of an object varies with time as shown in the graph below over a 5 second time interval.
If the object is initially at rest then
a)i) Calculate the velocity after 3 seconds.
ii) Calculate the velocity after 5 seconds.
b) Draw the corresponding velocity - time graph for the 5 second time interval on a piece of graph paper.
c) Calculate the displacement of the object after 5s. ( 32m)
Homework 4 – Equations of Motion
1) A car’s velocity increases from 10 ms-1 to 15 ms-1 in 2.5 seconds.
Calculate the acceleration of the car. ( 2.0ms-2)
2) An object accelerates uniformly at 3 ms-2 for 10 seconds and reaches a velocity of 35 ms-1.
Calculate the initial velocity of the object. ( 5ms-1)
3) A van moving in a straight line along a road accelerates uniformly from rest at 4 ms-2 and covers a displacement of 50 m.
How long will it take to travel the 50 m? ( 5s )
4) An object accelerates uniformly at 1.25 ms-2 from a velocity of 4 ms-1 to 6 ms-1.
What will the object’s displacement be? ( 8.0m)
5) A workman on the scaffolding outside one of the science classrooms drops a wrench. A physics student, bored with the lesson, times it as it falls past the classroom window. She found that it took 0.6s to fall past the 2m tall window. Calculate the spanner’s initial velocity as it appears at the top of the window. ( 0.40ms-1) (2)
6) A human cannonball at a circus is fired from the cannon with a muzzle velocity of 20ms-1 at 30° to the ground, and (hopefully) lands in a safety net that is at the same height as the mouth of the cannon.
(a) Calculate the horizontal and vertical components of the performer’s velocity. ( 17.3 and 10 ms-1) (2)
(b) How high above the net was he at his highest point? ( 5.1m ) (2)
(c) How far from the cannon should the net have been placed to safely catch the performer? ( 35.3m) (3)
(d) In practice, this distance would have to be slightly shorter. Why?
Homework 5 - Forces
1. A train made up of 3 carriages is pulled along a level track by a force of 16500N. Each of the carriages has a mass of 8000kg, and each experiences 1500N of resistive forces.
(a) Calculate the acceleration of the train.
(0.5ms-2)
(b) Work out the tension in link B. ( 11000 N ) (2)
2 . A cow has fallen over a cliff and cannot get back up to the field. The farmer has to rescue it by attaching a rope and harness, and lifting it using a pulley and his tractor (as shown in the diagram).
The tractor has a mass of 1500 kg, and the cow has a mass of 500 kg. The tractor’s engine can apply a force of 6000N. Ignore friction between the tractor and the ground.
(a) Calculate the initial acceleration of the tractor as it lifts the cow. ( 0.55 ms-2 ) (2)
(b) Draw a free body diagram showing the forces
acting on the cow as it is being lifted. (1)
(c) Calculate the tension in the rope lifting the cow.
( 5175 N ) (2)
4. In the diagram below, calculate the component of the weight acting down the slope. The mass of the trolley is 24 kg. ( 118 N )
4b) Calculate the acceleration of the trolley if frictional forces are ignored. ( 4.9 ms-2 )
4c) The acceleration is measured to be 2.5 ms-2 down the slope. Calculate the value of the frictional force acting. ( 58 N)
Homework 6 - Momentum And Impulse
1. In a rugby match, a 110kg forward in one team tackles an 85kg back in the other team. The forward is travelling at 5ms-1 and the back at 7ms-1 in the opposite direction when they collide and ‘stick’ together.
Take the direction of the forward as the positive direction.
(a) Calculate the velocity of the pair immediately
after the collision. ( -0.23ms-1) (2)
(b) Show by calculation whether this collision is elastic or inelastic. (2)
2. Explain, in terms of forces on the driver, why a seatbelt offers a far less damaging alternative to a steering wheel when a car stops suddenly during a collision. (2)
3. In a game of squash, a ball of mass 0.1 kg is moving towards the player with a velocity of 20ms-1. She strikes it with the racquet and it returns towards the wall at 40ms-1. If the time of contact between racquet and ball is 50ms, calculate the force applied on the ball by the racquet. ( 120 N ) (2)
4. A golfer strikes a
stationary golf ball, and
the force applied by the
club on the ball varies as
shown in the graph .
Use this graph to
determine the final
speed of the golf ball. The ball’s mass is 0.1kg. ( 40ms-1)
Homework 7 :Gravity
1) Calculate the force of attraction between yourself and someone sitting at a table next to you. (Estimate the masses of the people involved )
( c.a. 1x10-6 N )
2) Look up the radius of the moon and the gravitational field strength on its surface .(world wide wizard ) Estimate the mass of the moon. Check what we did in class to estimate the gravitational field strength and/ mass of the earth. ( 7.26x1022 kg )
3) Jupiter has a mass of 1.91 x 1027 kg and its radius is 7.14 x 107 m. What is the acceleration due to gravity on the surface of the Jupiter ? ( 25.8ms-2 )
4) What is the acceleration due to gravity at the centre of the earth ? ( assume it is a uniform sphere ). Explain your answer.
5) A satellite is orbiting the earth 4000 km above the surface of earth ( mass = 6.0 x1024 kg )or
1.037 x 107 m above the centre. What is the
acceleration due to gravity acting on the satellite? ( 3.7 ms-2)
( hint : look at the equations above and think )
Why does the satellite not crash into the earth’s surface ?
6) Using your knowledge of projectiles explain why a satellite remains in orbit around the earth. Remember there are two components of the motion to consider.
Homework 8 Special Relativity
1) State Einstein’s two postulates in Special Relativity.
2) A car is travelling east at 30 ms-1. A passenger in the car throws a ball up vertically and catches it 0.24 seconds later.
a) How high did the ball travel ? (0.07m)
b) Describe the motion of the ball relative to the person who threw it up.
c) Describe the motion of the ball relative to a stationary observer outside the car.
3) The Starship Enterprise is cruising the alpha quadrant at a uniform velocity of 2.5x108 ms-1 whilst Scotty fixes the Warp drive. Captain Kirk spots a stationary Klingon vessel. The Klingon captain measures the interior of her bridge to be 45m long. She takes 5seconds to complete this task. Calculate :
a) The length of the bridge according to Captain Kirk and ( 24.9m)
b) The time Scotty measures for the Klingon captain to measure her bridge. ( 9.04 s )
4) Luke Skywalker is sitting stationary , he measures the Millennium Falcon to be 75 m long as it whizzes by him. Hans Solo piloting the Millennium Falcon measures it to be 90 m long. How fast is Hans Travelling at ? (1.66 x 108ms-1)
Homework 9 The Expanding Universe
Speed of sound through air = 340 ms-1
Hubble :
1) A car horn emits a sound of 500 Hz when stationary.
a) Calculate the frequency of sound heard by a stationary observer when the car approaches at a speed of 20 ms-1. ( 531Hz)
b) What speed would the car recede at from the stationary observer for the frequency of the horn to drop to 450 Hz ?(37.8ms-1)
2) Explain what redshift is .
3) An astronomer measures a galaxy to be receding from earth at 1.2 x 106 ms-1.Calculate
a) the redshift ( 0.004 )
b) the distance the galaxy is from earth(1.74x1015 m )
c) the wavelength that a 650nm ( on earth ) line would be observed at from the galaxy. (652.6nm)
4) Give two pieces of evidence to support ‘Big Bang Theory’.
5. The table overleaf shows the values of lmax at different temperatures of the object. ( A ‘cold’ object gives out red light, when very hot it glows white hot : red and green and blue)
Temperature /K / lmax / m6000 / 4·8 × 10−7
5000 / 5·8 × 10−7
4000 / 7 3 × 10−7
3000 / 9·7 × 10−7
Kelvin is another unit of temperature, 00C =273 K
(a) Use this data to determine the relationship between temperature T and lmax .
(b) Use your answer to (a) to calculate:
(i) T of the star Sirius where lmax is 2·7 × 10−7m
(ii) The value of l maxfor the star Alpha Crucis which has a temperature of 23,000 K
(iii) T of the present universe when l max for the cosmic microwave radiation is measured as 1·1 × 10−3m.
(iv) The approximate wavelength and type of the radiation emitted by your skin, assumed to be at a temperature of 33 o C. ( to turn 0C into Kelvin add 273 to the temp in 0C )