Turning Effect of Forces

The diagram shows an athlete doing press-ups on a floor. The athlete is using both hands. The area of contact of each hand with the floor is $S$. The athlete’s toes act as a pivot during each press-up.

The athlete’s weight $W$ acts through point X. The distance between his toes and point X is three quarters of the distance between his toes and his shoulders.

What is the pressure exerted on the palm of each of the athlete’s hands?

Options

A   $\frac{W}{8S}$
B   $\frac{3W}{8S}$
C   $\frac{W}{4S}$
D   $\frac{3W}{4S}$

A student balances a non-uniform object on a pivot. To do this, a weight is suspended near the left-hand end of the object, as shown.

Where is the centre of gravity of the object?

Options

A long plank is pivoted at its centre of gravity.

Two objects, X and Y, are then placed on the plank.

X has a weight of $140\ \text{N}$ and is $1.2\ \text{m}$ to the left of the pivot. Y has a weight of $220\ \text{N}$ and is $0.55\ \text{m}$ to the right of the pivot.

A third object of weight $110\ \text{N}$ is placed on the plank so that the plank is in equilibrium.

On which part of the plank is the object placed?

Options

A   A
B   B
C   C
D   D

Which statement about centre of gravity is correct?

Options

A   Objects with a centre of gravity at the same height are less stable when the base is larger.
B   Objects with a centre of gravity at the same height are more stable when the base is larger.
C   Objects with higher centres of gravity and smaller bases are more stable.
D   Objects with identical bases are more stable when the centre of gravity is higher.

Which statements describing the moment of a force about a pivot are correct?

1. The moment of a force is a measure of the turning effect of the force.
2. The moment of a force is equal to the $\text{force} \times \text{perpendicular distance from the pivot}$.
3. The moment of a force is equal to the $\text{force} \times \text{pressure on the pivot}$.

Options

A   1 and 2
B   1 and 3
C   2 only
D   3 only

Four objects have identical shapes but different distributions of mass.

The centre of gravity of each object is shown by the dot marked G.

Which object is the most stable?

Options

A crane has a $5800\ \text{N}$ counterweight positioned $2.3\ \text{m}$ from the tower along a horizontal jib.

The centre of gravity P of the crane jib is marked.

What is the horizontal distance between the $2300\ \text{N}$ load and P so that there is no moment about P?

Options

A   $0.91\ \text{m}$
B   $3.5\ \text{m}$
C   $5.8\ \text{m}$
D   $8.1\ \text{m}$

A uniform beam is pivoted at its centre and balanced by three weights as shown.

What is distance $x$?

Options

A   $17.5\ \text{cm}$
B   $22.5\ \text{cm}$
C   $35.0\ \text{cm}$
D   $37.5\ \text{cm}$

A piece of card of uniform thickness and density is suspended freely from a horizontal pin. The diagram shows the card at rest.

Which cross is the centre of gravity of the card?

Options

A force $F$ is applied to a lever at distance $l$ from the pivot as shown.

Length $d$ is the perpendicular distance between the force and the pivot.

Which expression is the moment of force $F$ about the pivot?

Options

A   $\frac{F}{d}$
B   $\frac{F}{l}$
C   $F \times d$
D   $F \times l$