5th Mechanics Homework

Linear Motion


Section 1.

Q1. Define Speed, velocity, displacment. Give the units in which each are measured.

Q2. What are the SI units for the following quantities?   Time - Acceleration -Distance

Q3. How many second are in one day?

Q4. How mant seconds are in 5 years?

Q5. If a car is travelling at 100km/h change this value into the SI unit for Velocity.


Section 2.

Q1. What is the formula for velocity explain each part? Give also the unit for velocity and the unit of each part.

Q2. If a car travels a distance of 1200m in 30 seconds what is its velocity?

Q3. If a car travels at a velocity of 1.5 ms-1 for a time of 50 seconds how far will the car have traveled?

Q4. If the speed of a runner is 50cm per second how far will she have moved in one minute?

Q5. If a car is travelling at 120 kmh-1 how far will it have moved in 1.5 hours?

Q6. If a cyclist is moving for 5 minutes at a speed of 2.5 ms-1 how far will she have moved in this time?


Section 3.

Q1. Write down the formula for acceleration and explain each part. give also the units of each part and the unit of acceleration.

Q2. If a car starts at a velocity of 1m/s and accelerates to 3m/s in a time of 25 seconds what is the acceleration of the car?

Q3. If a cyclist starts from rest and accelerates to a speed of 2.5ms-1 in a time of 13 seconds what will their acceleration be?

Q4. A race car starts from rest and accelerates to 200km/h in a time of 6 seconds find the cars acceleration.

Q5. A bullet is fired from a gun and reaches a speed of 250kmh-1 in 100 milliseconds, find the acceleration of the bullet.


Section 4.

Q1. A missle is given an acceleration of 20 ms-2 and is fired at a target 2km away at what velocity will it be travelling when it hits its target?

Q2. A high speed train starts in Paris and travels to Lyon in 2 hours. Lyon is 350km from Paris. At what speed is the train travelling when it is at its fastest? Write your answer in Kmh-1.

Q3. A gun fires a bullet which hits its target at a distance of 1.5km 5 seconds later. what is the bullets velocity when it hits the target? 

Q4. A person has a gun in one hand and a bullet in the other. The person fires the gun and at the same time drops the bullet from the same height as the gun was fired at. Which bullet will hit the ground first assuming the fired bullet doesnt hit any target?

Q5. Why do any objects that are moving stop unless a force continues to act on it?


Section 5. 

Q1. A dense metal ball is dropped over a cliff and hits the ground 5 seconds later. What acceleration has the ball got? Find also the height of the cliff. What speed will the ball be travelling at the instant before it hits the ground?

Q2. A cliff is 400m high a rock falls over the side of it how long will it take it to hit the sea below?

Q3. A student throws a ball into the air with an initial velocity of 5m/s how long will it take for it to reach its maximum height? How high will the ball go?

Q4. A ball is thrown upward with an initial speed of 4 m/s how long will it take for the ball to hit the ground again? (hint separate the problem)

Q5. A ball is located 20m from the edge of a cliff of height 200m. The wind blows and the ball gets an acceleration of 1.5ms-1. When it reaches the edge of the cliff the ball falls over. How long does it take for the ball to travel from the start point and hit the sea below?

Section 6.

Q1. Draw a distance time graph which shows an object moving 200m from a fixed point in 3 seconds, resting there for 5 seconds and then returning to the original point in a time of 8 seconds.

Q2. Draw a velocity time graph which shows an object accelerate up to a velocity of 10ms-1 in a time of 5 seconds and remain at that constant velocity for 10 seconds and then decelerate to 0m/s in a time of 1 second.

Q3. What does the area under the line of a velocity time graph give you?

Q4. What does the slope of a velocity time graph give you?

Q5. For the graph sketch in Q2 find the acceleration and deceleration of the object in question. Find also the total distance travelled by the described object.

Force and Momentum

Section 7. 

Q1. Find the force acting on an object if it has mass of 25kg and acceleration of 2m/s/s.

Q2. Find the mass of a body with acceleration 5ms-2 experiencing a force of 3N.

Q3. If an object of mass 100kg has a force of 25N pulling it to the right and a force of 34N pulling it to the left what direction will the block travel in? Find also the acceleration of the block in the direction you have mentioned.

Q4. What is friction?

Q5. If an object has a mass of 60kg and a velocity of 5m/s find its momentum.

Section 8.

Q1. A cannon of mass 1000kg fires a cannon ball of mass 80kg at a velocity of 17ms-1. Calculate the speed at which the cannon will jump backward.

Q2. A student of mass 90kg steps off a fishing boat of mass 500kg at a speed of 1.5ms-1 at what velocity will the boat move away from the pier?

Q3. A Ford of mass 1.35 tons travelling at 30kmh-1 has a head on collision with a Toyota of mass 1.1 tons travelling at 55km\h. In which direction will the two cars travel after the collision? At what speed will the combined mass travel after the crash?

Q4. A lorry with mass of 5 tons and velocity of 50kmh-1 crashes into a parked car of mass 1.2 tons find the velocity at which the combined mass moves at after the crash.

Q5. A truck with mass 10 tons and a velocity of 55kmh-1 hits directly into the back of a car of mass 1 ton travelling at 30kmh-1 in the same direction. At what speed are they both travelling after the crash?

Density & Pressure

Section 9.

Q1. Define density. Define pressure and give the units of each quantity.

Q2. Find the density of an a subsatnce with mass 20kg and volume 2 m3.

Q3. Find the density of a substance with mass 546g and volume of 20 cm3.

Q4. What pressure is applied by an object exerting a force of 150 N over an area of 1 square meter?

Q5. What pressure is applied by an object of mass 25kg over an area of 20 cm2.


Section 10.

Density of water = 1000kg/m3

Q1. What is the reason an object will sink or float in a liquid?

Q2. An object is at a depth of 2.5 meters in water. What is the pressure on the object?

Q3. The top of a cube of side 25cm is at a depth of 1.5m in water find the pressure at the top and at the bottom of the cube. Find also the upward force experienced by the cube.

Q4. The bottom of a cubic block of side 75cm is at a depth of 5.2m in water. Find the pressure due to the water at the top and the bottom of the block. What is the upthrust experienced by the block?

If the block has a wieght of 10N will it sink or float?

Q5. State Archemede's law.


Section 11.

Q1. What is the law of floatation?

Q2. State Boyle's law.

Q3. State Newton's universal law of gravitation. Write the formula too. What are the units?

Q4. What is the force of attraction between two masses of mass 2kg standing 2m appart.

Q5. What is the force of attraction between two masses of mass 10 tons standing 1mm apart?

Section 12. 

Mass of Earth 6x10 24kg...Mass of moon 7x10 22kg...Radius of Earth 6.4x10 6m... Radius of Moon 1.7x10 6 m

Q1. Calculate the acceleration due to gravity of a 60kg person on the surface of the Earth.

Q2. Find acceleration due to gravity of the same person at a height of 1000km above the earths surface.

Q3. Did the fact that you had the persons mass make any difference in answering Q1 & Q2 above? Explain your answer.

Q4. Find acceleration due to gravity on the moon.

Q5. Find the magnatude of the gravitational pull between the Earth and the Moon considering the surfaces of both bodies are 300,000km apart.

Section 13.

Q1. What is torque? Give some examples of where torgue is applied.

Q2. What is a lever? Give some everyday examples of levers.

Q3. A door handle is 20cm long from the fulcrum to the end of the handle. If a force of 20N is applied to the end of the handle, what is the moment around the door handle?

Q4. A stone has a mass of 200kg. Describe using calculations and a diagram how you could use a lever to move the stone.

Q5.  If a gas is compressed to 1/3rd its original volume of 100cm cubed what will the pressure be if it was 200 Pascals in the begining?


Work Energy and Power


Section 14. 

Q1. Name some forms of energy. Give the unit that energy is measured in. What other units is the unit for energy made up of?

Q2. If an object is dropped from a helicopter which is at a height of 550m and it has a mass of 20kg what potential energy does the object have?

Q3. What kinetic energy does the object from Q2 have just before it hits the ground? What speed is the object travelling at?

Q4. If an object of mass 200kg is moved a distance of 150m in a time of 30 seconds what power was used to move the object?

Q5. A pendulum has a length of 3m and it is set to swing with an angle of 45 degrees. Find the maximum potential and kinetic energy the pendulum bob will have, find also the maxium speed at which the bob will be travelling.

 At what speed will the bob be travelling when its potential energy is at a maximum? 

Find the speed of the pendulum when it is half way from the rest position and the Ep Max Position.

(Pendulum mass = 5kg).


Section 15.

Q1.Find the moment of force around the handles of a bicycle which are 0.5m appart and are experiencing a couple of force of 3N. Give another name for this moment of force.

Q2. Name some renewable and non renewable forms of energy. Explain what the terms renewable and non renewable mean.

Q3. Give some advantages and some disadvantages of Nuclear energy.

Q4. A person carries 20kg blocks up a flight of stairs in 25 seconds. If there are 90 blocks in all how much work is done by the person? What power is the person using during the job?

Q5. A heater uses 2500 watts of power when in operation. Only 1895 watts of this power is actually7 converted to heat. What is the overall percentage efficiency of the heater?

Section 16.

Q1. A horizontal force is exerted on a car. The force is 400N and the car moves 150m find the work done by the force.

Q2. A man raises a mass of 60kg 85cm 65 times in one minute. Find the work done by the man. Find also the power exerted by the man.

Q3. A 1000kg car accelerates from 0 - 100 kmh-1 in a time of 45 seconds. Find the work done by the engine.

Q4. The input power to a cars wheels is 8kw but only 7.85kw is seen as actual turning power. What is the percentage efficiency of the car?

Q5. A basketball hoop is 2.35m in height and a basketball which is resting on it and about to fall has a mass of 795g. Find the potential and kinetic energy of the ball. What speed will the ball be traveling at just befor it hits the ground?

Section 17.

Q1. Find the mass of the stick.

Q2. Find the forces acting around the 0cm, 25cm, 60cm and 95cm marks on the stick.

Q3. Is the stick balanced?


Circular Motion.

Earth mass = 6 x 1024 kg                   Mass of moon= 7 X 1022 kg

Earth radius = 6.4 X 106 m               Radius of moon = 1.7 X 106 m

Distance from earth rim to moon surface = 3.7 X 108 m

Gravitational constant = 6.7 X 10-11 N m2 Kg-2.


Section 18.

Q1. Define angular velocity (give units)

Q2. What is centripetal acceleration?

Q3. A car of mass 1000kg  travels round a circular bend of radius 150m at 100kmh-1. What is the force on the car towards the centre of the bend?

Q4. State Newton’s law of gravitation.

Section 19.

Formulae = Angular Velocity = Rate of change of an angle.       Units = rads-1.            ω = Ө / t   or  Ө = ωt    ω = v / r         


Q1. If an angle is traced out at 2 radians per second how long will it take to make one revolution?

Q2. If an object is travelling at 5 ms-1 in a circle of radius 5m what is the objects angular velocity?

Q3. If a particle of mass 2kg moving in a circle of radius 3m under a centripetal force of 10N what is the velocity of the particle? Give both angular and linear velocity in your answer.


Section 20.

Formulae:  F = mv2/r        or        F = mrω2              V2 = GM / R            T = 2πR / v       or     T2 = 4π2R3 / GM

Q1. If a satellite orbits the earth 285 km above its surface and has a mass of 390907 kg at what linear speed is the satellite travelling at?

Q2. At what speed are you travelling at right now at the surface of the earth?

Q3. If a satellite is in geostationary orbit how long will it take for the satellite to complete one full revolution?

We know that to be in geostationary orbit (parking orbit) means that the satellite must be 36,000km from the earth’s surface.


Calculate the mass of the earth from this information.

Simple Harmonic motion.

Formulae: F = -ks    a = - W2S    T = 1/f     F = 1/T    T = 2π/ω     T = 2π √(L/g) 


Section 21.

Q1. State Hooke's Law.

Q2. A system which obeys Hooke's law has an elastic constant of 2000Nm-1, Find the displacement when the force is 300N.

Q3. When is a body said to be in simple harmonic motion?

Q4. The acceleration of a particle executing simple harmonic motion is 5ms-1, when it is 30cm from the equilibrium position.

What is its acceleration when it is 10cm from the equilibrium position?

What is its distance from the equilibrium position when its acceleration is 1.2ms-2?

Section 22.

Q1. The period of a particle executing simple harmonic motion is 4 seconds. What is its acceleration when it is 20cm from the equilibrium position?

Q2. In an experiment to calculate acceleration due to gravity using a simple pendulum, what was the equation used to calculate the acceleration?

What would the student calculate acceleration due to gravity to be if the length of the pendulum was 50cm and the period was 2 seconds?

Q3. Why was a dense heavy bob used in this experiment and why would the student have placed the pendulum string between two coins?

ue to gravity to be if the length of the pendulum was 50cm and the period was 2 seconds?

Q4. How was the length of the pendulum measured?

Vectors & Scalars

Section 23.

Q1. Define what a vector quantity is?

Q2. Define what a scalar quantity is?

Q3. Describe an experiment that you could carry out in the lab to show the resultant of three vectors.

Q4. If a ship is sailing north at 10ms-1 and the flow of the sea is 3ms-1 to the east, what will the overall displacement of the ship be and in which direction will the ship have gone after one second and after an hour?

Q5. A swimmer crosses a river which is 200m wide he crosses the river at a speed of 2ms-1. The river is flowing with a velocity of 0.5ms-1. How many meters down the river will the swimmer find themselves after the crossing?

Section 24.

Section 25.

Section 26.

Q1. Use a diagram to show how a vector could be broken into its perpendicular components. 

Q2. Write down the two formulae you would use in order to breakdown a vector into its perpendicular components.

Q3. Break a vector of magnitude 200 Newtons into its perpendicular components.

Q4. A pendulum is set to swing at 35 degrees from its rest position break to motion of the pendulum into perpendicular components