Simple machines - Answer key

Fluency

Lever, inclined plane, wedge, screw, pulley, wheel and axle.
$F_L d_L = F_E d_E$ .
Fulcrum: the wheel at the front. Effort: handles (lifted by person). Load: weight of material in tray. Class 2 (load between fulcrum and effort).
The ratio of the load force to the effort force — how many times the machine multiplies your effort.
$\text{MA} = 200/50 = 4$ .
$300 \times 0.5 = F_E \times 1.5 \Rightarrow F_E = 150/1.5 = 100$ N.
$100 \times 1 = F_E \times 4 \Rightarrow F_E = 25$ N.
Tweezers, fishing rod, human forearm lifting a weight, a broom.
Direction only.
An inclined plane.

Reasoning

A ramp lets you apply a smaller force over a longer distance. The work done (force × distance) is about the same either way, but the smaller force is achievable by one person.
The lever rule $F_L d_L = F_E d_E$ can be rearranged to $F_E = F_L \times d_L/d_E$ . For $F_E < F_L$ (that is, MA > 1), the denominator must be larger, so $d_E > d_L$ .
MA = 3 means the effort is $1/3$ of the load. In return, the rope pulled is $3$ times the distance the load moves.
The lever rule requires $F_L d_L = F_E d_E$ . If the weights are fixed, a heavier load must sit at a shorter distance from the fulcrum to balance the lighter person at a longer distance.
Friction at the fulcrum, along ramps, and in pulley bearings converts some of the input work to heat. Real MA is always slightly less than ideal MA.
The nail is the load, the hammer’s head is the fulcrum, and your hand on the handle applies the effort. The long handle and short claw give a large effort arm : load arm ratio — high MA.

Reasoning

Weights: $60 \times 10 = 600$ N and $40 \times 10 = 400$ N. Let $d$ be distance for the $40$ kg child. $600 \times 2 = 400 \times d \Rightarrow d = 3$ m. But the see-saw is only $4$ m long with the fulcrum in the middle — $2$ m each side. So balance is impossible unless the fulcrum is moved. (Good — forces students to notice infeasibility.)
Ideal: work in = work out. $500 \times 1.2 = 150 \times L \Rightarrow L = 600/150 = 4$ m.
Effort: $600/4 = 150$ N. Rope pulled: $4 \times 2 = 8$ m.
Class 2 lever — the load (nut) is between the fulcrum (hinge) and the effort (hands).

Reasoning

Low gear (small front ring + large rear ring) gives a high MA: your pedal force at the chain is multiplied at the wheel, so climbing a hill needs less effort per pedal stroke, but you pedal more times for each wheel turn. High gear is the reverse: less force multiplication but the wheel turns further per pedal stroke — useful at speed on flat roads.
Yes — balance depends only on torque ratio, not absolute distances. $50 \times 0.2 = 50 \times 0.2$ . It still balances.
Ideal effort: $400 \times 1 / 4 = 100$ N. With $20\%$ loss, work in = $400$ J / $0.8 = 500$ J. Actual effort $= 500/4 = 125$ N. Efficiency = $400/500 = 80\%$ .
Pulley systems scale well with large MA in a small footprint and are safer than levers for tall buildings. Crane levers require long rigid arms and huge counterweights. Pulleys also allow workers to stand safely away from the load. Trade-offs: pulleys can jam, need strong ropes, and have more friction; cranes lift faster.

Year 7 answers