A wheel and axle arrangement has an axle with a diameter of 25cm. A rope is wrapped around the axle and is supporting a load of 2 tonnes.
1) If the mechanical advantage of the system is 30, determine the diameter of the wheel___________m.
2)Determine the effort required to maintain the system equilibrium ______N.
Need a little help with the formulas. Thanks.
To find the diameter of the wheel in the wheel and axle system, we can use the formula for mechanical advantage:
Mechanical Advantage (MA) = Diameter of Wheel (DW) / Diameter of Axle (DA)
In this case, we are given that the mechanical advantage is 30 and the diameter of the axle is 25 cm. Let's substitute these values into the formula and solve for the diameter of the wheel:
30 = DW / 25
To isolate DW, we can multiply both sides of the equation by 25:
30 * 25 = DW
Therefore, the diameter of the wheel is 750 cm.
To determine the effort required to maintain the system in equilibrium, we can use the formula for mechanical advantage again:
Mechanical Advantage (MA) = Load (L) / Effort (E)
In this case, we are given that the load is 2 tonnes or 2000 kg. Let's substitute these values into the formula and solve for the effort:
30 = 2000 / E
To isolate E, we can multiply both sides of the equation by E:
30E = 2000
Then, divide both sides of the equation by 30:
E = 2000 / 30
Therefore, the effort required to maintain the system in equilibrium is approximately 66.67 Newtons.