School stuff

Answers to practising moments sheet

Remember: the moment of a force is the force (N) x distance from the fulcrum (pivot point).

To calculate extra weight needed on the mobile:

    • Remember that anticlockwise moments equal clockwise moments when it is balanced
    • Calculate anticlockwise moments (caused by 5N ball) = 5N x 25cm = 125Ncm
    • Calculate clockwise moments (caused by 2N ball) = 2N x 10cm = 20Ncm
    • Calculate extra clockwise moment needed by 3rd ball = 125Ncm-20Ncm = 105Ncm
    • Calculate weight needed at 25cm to give this extra moment. 105Ncm/25cm = 4.2N
  1. Bob carries his ladder home:
    • The weight of the ladder acts at the centre of mass/gravity.
    • The fulcrum is Bob’s shoulder where the ladder rests.
    • The turning moment caused by the weight of the ladder = 400N x 50cm = 20,000Ncm (clockwise)
    • Bob needs to provide an anticlockwise moment of 20,000Ncm. His hand is 30cm from the fulcrum so the force must be 20,000/30 = 667N downwards.
    • To reduce the force needed his hand should be moved further from the fulcrum (his shoulder)
    • Bob will hang the paint in front of him of course, but how far away? It needs to provide a moment of 20,000Ncm to balance the ladder. It weighs 50N so needs to be 20,000/50 = 400cm away from the fulcrum. This is a problem because the ladder is not that long!
    • Extra question: What should Bob do to balance the ladder more easily on his shoulder?

  1. As Jim walks forward the force needed will increase as the distance from the fulcrum (other end of the ladder) gets less. He needs to provide the same turning moment but is closer to the fulcrum. When he reaches the middle of the ladder the other end will lift up and he will be left holding the entire weight of the ladder on his own!

Pressure and Density Practice Questions

  1. The Mass of you and your chair is 40kg.
    • To convert to weight in newtons we multiply by 10 on Earth because each kg is attracted by the earth with a force of 10N. The answer is therefore 400N.
    • Pressure = Force/area. Force in this case is the weight. The weight is spread over 4 legs evenly so the weight on each leg is only 100N. The area is 3cm2.. Pressure = 100N/3cm2 = 33.3N/cm2.
  2. A quadbike has wide tyres to spread the weight over a larger area. This reduces the pressure on the ground and therefore stops it sinking into the mud or sand or whatever it is on.
  3. Remember that the class of a lever depends on what is in the middle. FLE.
    • Fulcrum in middle = 1st class
    • Load in middle = 2nd class
    • Effort in middle = 3rd class
    • A nutcracker is hinged at one end with the load in the middle so is 2nd class. It is in fact two levers joined together at the fulcrum
    • A pair of pliers has the fulcrum at the centre so is 1st class. Again, two levers joined together.
  4. Oil has a density of about 0.9g/cm3, less than water. We know this because it floats on water and so must be less dense than water.
  5. Cold water sinks because its molecules are closer together and so its density is higher than warm water. The warm water floats on the cold water.
  6. Mercury is a metal, liquid at room temperature, which is very dense.
    • If each cm3 has a mass of 13.6g then 100cm3 must have a mass of 13.6 x 100 = 1360g = 1.36kg
    • To convert to weight, multiply mass in kg by 10, so 1.36 x 10 = 13.6N
  7. Your density when you float is less than water i.e. slightly less than 1g/cm3. When you breathe out your density increases to slightly more than 1g/cm3 so you sink. The density changes because you change your volume slightly when your chest cage falls and moves in. This makes you take up less space and so you become more dense.