Introduction to mechanical systems practice questions.

A pair of barbecue tongs pivots at its closed end, the hand squeezes the arms a short way from that pivot, and the food is gripped at the open end. Which statement gives the lever class of one arm together with the correct arrangement of pivot, effort and load?

• First class, with the pivot between the effort and the load
• Second class, with the load between the pivot and the effort
• Third class, with the effort between the pivot and the load
• Third class, with the load positioned between the pivot and the effort

Answer: Third class, with the effort between the pivot and the load

The class is fixed by which of the three points lies in the middle, and in tongs the effort does, so the mechanical advantage is below one and the hand has to push harder than the grip it produces. What is bought instead is movement: the tip travels further and faster than the hand.

A flat belt runs over two smooth pulleys and transmits the drive by friction alone. Which consequence follows from that for the drive?

• The two shafts are held exactly in step whatever the load on the output
• The output shaft turns in the opposite direction to the input shaft
• The belt carries no drive at all until the pulleys reach their working speed
• The ratio of the two shaft speeds is not held exactly, because the belt can creep

Answer: The ratio of the two shaft speeds is not held exactly, because the belt can creep

A friction drive is not a positive drive: the grip depends on the tension in the belt and on the load, so the belt creeps a little on the pulley face and the output speed drifts below the value the pulley diameters predict. A drive that engages on teeth cannot do this, which is why timing jobs never use a plain flat belt.

The arm of a windscreen wiper swings to and fro through an arc about a fixed pivot while the motor runs. Which type of motion does the arm have?

• Rotary motion
• Linear motion
• Reciprocating motion
• Oscillating motion

Answer: Oscillating motion

Oscillating motion swings backwards and forwards about a pivot, whereas reciprocating motion moves backwards and forwards along a straight line, as a piston does. The arm never completes a revolution, so the motion is not rotary, and it does not travel in one direction along a line, so it is not linear.

In a spur gear pair the driven gear is replaced by one with twice as many teeth, while the driver gear and the input speed are unchanged. Ignoring losses, what happens at the output shaft?

• The output turns at twice the speed and delivers half the torque.
• The output turns at twice the speed and delivers twice the torque.
• The output turns at half the speed and delivers twice the torque.
• The output turns at half the speed and delivers half the torque.

Answer: The output turns at half the speed and delivers twice the torque.

Gear ratio = teeth(driven)/teeth(driver), so doubling the driven teeth doubles the ratio and n_out = n_in/GR halves. The common error is to read more teeth as more speed: the power is unchanged, so what the output loses in speed it gains in torque.

A 25-tooth gear on a motor shaft meshes with a 75-tooth gear on the output shaft. A student writes: 'gear ratio = 75/25 = 3, so the output shaft turns three times faster than the motor shaft.' Identify the error in the statement.

• The ratio is right, but a ratio above one means the output turns three times slower.
• The ratio should be 25 divided by 75, and the output turns three times faster.
• The ratio is right, and the torque at the output is three times smaller.
• The ratio should be 25 divided by 75, and the output torque is three times larger.

Answer: The ratio is right, but a ratio above one means the output turns three times slower.

The arithmetic is correct - GR = teeth(driven)/teeth(driver) = 3 - but the interpretation is inverted: n_out = n_in/GR, so a 3:1 step-down drive turns the output at a third of the input speed while multiplying the torque by three.

While testing a machine a student records that the effort moves 800 mm while the load rises 200 mm, and writes: 'mechanical advantage = 800/200 = 4'. Identify the error in the statement.

• The two distances are the right way round, but the answer should be 0.25.
• Those two distances give the velocity ratio, not the mechanical advantage.
• The distances give the efficiency of the machine, expressed as a ratio.
• The load distance must be divided by the effort distance to give 0.25.

Answer: Those two distances give the velocity ratio, not the mechanical advantage.

MA = load/effort and is obtained from two forces; VR = d_effort/d_load and is obtained from two distances, so this figure of 4 is the velocity ratio. Taking it as the mechanical advantage would make every machine appear exactly 100 per cent efficient, since efficiency = MA/VR.