My niece is struggling with some mechanics questions, but the last time I formally studied maths was many years ago! If anyone could help me understand any of the questions with working out as well as explanations, that would be great!
(Please note that I have managed to draw some diagrams for her. It is more so the mathematical methods that I lack understanding of.)
1. A cube of mass 7 kg rests on top of a horizontal table. A smaller cube of mass 3kg is placed on top of the 7kg cube.
Find the reaction between the two cubes and that between the larger cube and the table.
2. A particle of mass m rests on a smooth horizontal table. It is connected by a light inextensible string which passes over a smooth pulley at the edge of the table to a particle of mass m that hangs freely. The system is released from rest.
Find the distance travelled and the speed at the end of the first 0.5 seconds of motion.
3. Particles of mass 700g and 500g are connected by a light inextensible string passing over a smooth pulley. Initially, both masses hang vertically, 20cm above the ground.
If the system is released from rest, find the greatest height reached above the ground by the 500g mass.
I appreciate any bit of help! Thanks in advance.
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For question 1, the following, together with Newton's third law of motion, should help:
For question 2, note that the total mass is 2m and this is undergoing a constant acceleration due to gravity. The constant acceleration equations allow the velocity, v, at any time to be written as: v = u + at, where u is initial velocity, a is acceleration (due to gravity here) and t is time interval.
For question 3, note that the 700g mass is being pulled down by gravity as is the 500g mass. However, because they are on opposite sides of a pulley, there will be a net force of (0.7 - 0.5)*9.8 N pulling the 700g mass downwards and the 500g mass upwards. Find the time it takes the 700g mass to reach the floor using s = ut + (1/2)at2, where s is the distance (20cm). Find the velocity of both 700g and 500g (the same for both, of course) from v1 = u + at. This will act as the initial upward velocity for the 500g mass which will carry on rising against gravity, but slowing until it comes to a stop.
Use 0 = v12 + 2as to find the extra distance, s, travelled by the 500g mass. Don't forget to add on the 20cm to get the total height, and to use -9.8m/s2 for gravitational acceleration in this part (as the mass is travelling in the opposite direction from that in which gravity is acting).