Inclined Plane

An inclined plane is a sloping surface used for pulling or pushing a load up, rather than lifting them vertically.

Velocity Ratio =Distance moved by EffortDistance moved by Load=xh

Velocity Ratio =1sinθ

Hydraulic Press

Definition of Hydraulic Press

Hydraulic press is a device used to produce a very large force to compress or lift up a heavy load. It is used in the printing press where a large force presses the type with ink on it against the paper. Pressure is transmitted equally to all parts of a liquid at the same level.

Animation: Observe and explain what is going on using the comment box:

If A₁ is the area of small piston and A₂ area of the large piston, pressure(P) is transmitted equally at the same level, then

P=EA1,E=P×A1P=LA2,L=P×A2

Therefore a small effort lifts a large load.

M.A=LE=A2A1=R2r2

If x and y are the distances moved by E and L respectively,  A₁x = A₂y

xy=A2A1=R2r2=V.R

Example 2:

An inclined plane of angle 15⁰ is used to raise a load of 4500N through a height of 2m. If the plane is 75% efficient, calculate (i) Velocity ratio of the plane (ii) Work done on the load

Solution:

M.A=LE=A2A1=R2r2LE=A2A1L=A2×EA1=200×4010=800N

EVALUATION

A man pulls up a box of mass 70kg using an inclined plane of effective length 5m onto a platform      2.5m high at uniform speed. If the frictional force between the box and the plane is 100N, draw the diagram of all the forces acting on the box when in motion and calculate the

(i) Minimum effort applied in pulling up the box

(ii) Velocity ratio of the plane

(iii) Mechanical advantage of the plane

(iv) Efficiency of the plane

(v) Energy lost in the system

(vi) Work output of the man

(vii) power developed by the man given that the time taken to raise the box onto the platform is 50s. ( g = 10m/s²)

Screw

Definition of Screw

A screw is mechanical fastening device consisting essentially of an inclined plane wound spirally around a cylinder or a cone. The ridges formed by the winding planes are called threads, and depending on the intended use, the threads may be square, triangular, or rounded in cross section.

Parts of a Screw Thread

A screw thread is made of the following parts:

1. Thread or Lead: Is the distance along the screw’s axis that is covered by one complete rotation of the screw (360°).
2. Pitch: The distance between two corresponding points on adjacent threads
3. Plane or Start : It can be Single-start or double-start. Single-start- means that there is only one “ridge” wrapped around the cylinder of the screw’s body.Double-start” -means that there are two “ridges” wrapped around the cylinder of the screw’s body Each time that the screw’s body rotates one turn (360°), it has advanced axially by the width of two ridges.

Another application of the screw is Screw jack, Ratchet brace.
When a screw is turned through one complete revolution by the application of an effort ( on the screw head, using the handle of the ratchet brace, or the Tommy bar of the screw jack), the load moves a distance equal to the pitch(P), which is the distance between consecutive threads.

V.R=2πRP

R = Radius of the screw or length of the handle of the ratchet brace of length of the tommy bar.