Classical Mechanics Answers

1. A student carries out an experiment to find the specific heat capacity of a liquid.  The results from the experiment were as follows

Initial temperature = 19⁰

Final temperature = 35⁰C

Mass of liquid = 2kg

Power of heater = 350W

Time heater on = 5min

a)     Calculate the energy supplied by the heater

b)     Calculate the specific heat capacity of the liquid

c)     On reviewing the experiment the student found that the container of the liquid was a poor insulator of heat.  Would the calculated value of the specific heat capacity of the liquid be higher or lower than the actual value?

1. Calculate the amount of energy required to raise the temperature of
2. 0.5kg of water from 20⁰C to 65⁰C.  (Specific heat capacity of water = 4180J/kg⁰C)
3. A 950g steel baking tray from 18⁰C to 183⁰C.  (Specific heat capacity of steel = 500J/kg⁰C)

1. A well insulated kettle contains 1.2kg of water at a temperature of 20⁰C.  The kettle is switched on and takes 180s to come to the boil. (Specific heat capacity of water = 4180J/kg⁰C)
2. How much energy is absorbed by the water in 180s?
3. Calculate the power rating of the kettle.
4. A cheaper kettle is not so well insulated, what effect will this have on the time to heat the water?

1. The tip of the soldering iron is made of copper with a mass of 30 g.  Calculate how much heat energy is required to heat up the tip of a soldering iron by 400 °C.

(specific heat capacity of copper = 380 J/kg°C)

1. A kettle uses 167200J of heat energy when it heats water from 20⁰C to 100⁰C.  How much water is in the kettle? The specific heat capacity of water is 4180j/kg⁰C.

1. The temperature of a 0.8 kg metal block is raised from 27 °C to 77 °C when 4200 J of energy is supplied.  Find the specific heat capacity of the metal.

1. 9600 J of heat energy is supplied to 1 kg of methylated spirit in a polystyrene cup.

Calculate the rise in temperature produced.

Take the specific heat capacity of methylated spirit to be 2300 J/kg°C.

1. A 750g steel cooking pan cools from 65⁰C to 18⁰C.  How much heat energy is released by the pan?  The specific heat capacity of steel is 500j/kg⁰C.

1. An insulated container contains 0.5kg of water at an initial temperature of 16⁰C.  A heater is placed in the water and switched on.  It supplies 83600J to the water.  Calculate the final temperature of the water.  (Specific heat capacity of water = 4180J/kg⁰C)

1. A car of mass 1000kg, travelling at 20ms^-1 is brought to rest on 40s.  What is the power of the brakes?

1. A pupil of mass 50kg climbs stairs of vertical height 7m in a time of 9s.  What power does the student have in climbing the stairs?

1. A 2kW motor pulls a load of 3000N for 8m.  How long does it take?

1. A man pushes a wheelbarrow for 60 m using a 50 N force. If he takes 10 s, what is his average power?

1. A machine lifts a load of 4000 N to a height of 5 m in 20 s. What is its power?

1. A lift can raise a total mass of 800 kg up 10 m in 40 s. What is its power?

1. What is the efficiency of a machine which has a power input of 800 W and a power output of 600 W?

1. How efficient is a machine that takes in 24000J of energy and produces 8000J of useful energy?

1. How efficient is a machine that takes in 24000J of energy and produces 8000J of useful energy?

1. A machine which is 70% efficient has a power input of 360W.  What is the power output?

1. A motor which is 60% efficient has an output power of 480 W. What is its input power?

1. An electric motor rated at 500 W runs for 2 minutes and does 45 kJ of work.

a)     What is its input energy?

b)     What is its efficiency?

1. What is the efficiency of a motor rated at 750 W which can lift a 25 kg load to a height of 4 m in 2 s?

In a ball game a 70 kg player is running at 10 m/s when he is hit by the other player he bounces off in the opposite direction at 2 m/s. What is the players change in momentum?

A Stationary lift raft with mass of 160 kg is carrying two survivors with masses of 55 kg and 72 kg, they dive off raft at the same instant the 55 kg person due east at 4.4 m/s and the 72 kg person due north at 4.2 m/s. At what speed and in what direction does the raft start to move?

A 1200 kg car traveling at 15 m/s due east collides with a 720 kg car traveling at 21 m/s due north. As a result of the collision the two cars lock together what is the velocity immediately after the collision?

75 kg ball player moving at a velocity of 7.8m/s hits a player moving in the opposite direction who has a mass of 90 kg. If they collide and stop to have a speed of zero how fast is the other player moving originally?

A particle P carries a charge e and moves under the influence of static magnetic field B(r) which exerts the force F × ev × B

on P, where v is the velocity of P . Show that P travels with constant speed.