An electroscope is a device that can be used to detect or measure the amount of charge in its vicinity. One of the earliest electroscopes is the gold-leaf electroscope which was invented by a British clergyman Abraham Bennet. This is a cheaper model of the leaf electroscope made using aluminum foil. Materials

1. Paper clip
2. Aluminum foil
3. Modelling clay
4. Glass bottle with a narrow neck
5. Steel or brass sinker

Procedure

1. Cut two strips of aluminum foil measuring 2 cm by 0.5 cm.
2. Straighten the paper clip before bending both ends to make two hooks. Hang the paper clip using one hook from the sinker.
3. Pierce each aluminum strip at one end through the other hook of the paper clip, leaving it to hang from the hook.
4. Place the paper clip and aluminum strips inside the bottle. If the sinker is smaller than the neck of the bottle, use some modeling clay to keep it in place.
5. Now you can test the electroscope by rubbing a comb with some wool and placing it near the paper clip.

Science Explained

Negative charges (electrons) are deposited on the comb by rubbing with wool. When the comb is placed near the sinker without touching, the negative charges in the sinker are repelled. As glass is an electric insulator, the only way for them to go is downwards onto the aluminum strips. Both strips are now negatively charged and will repel each other. The extent of their repulsion is dependent on the amount of charge on the comb and its distance from the electroscope.

Hans Christian Oersted showed that an electric current can affect a compass needle in 1820. This confirms the direct relationship between electricity and magnetism, which in turn, paved the way for further understanding of the two. The direction of the magnetic field can be changed by flipping the wire around, which suggests that the direction of the magnetic field is dependent on the direction of current flow. Materials

1. 1.5V Battery
2. Wire
3. Compass

Procedure

1. Place the compass on a horizontal surface.
2. Connect the wire to both ends of the battery.
3. Place the middle of the wire directly over the compass, parallel to the initial orientation of the needle.
4. Observe the needle deflect to one direction.
5. Now flip the wire over so the current flows in the opposite direction and place it over the compass again.
6. The needle will deflect in the other direction.
7. Additionally, you can place the compass on top of the wire now.

Science Explained A current will carry with it its own magnetic field. The magnetic field lines form concentric circles around the wire so that the field points in one direction above the wire and the opposite direction below the wire. Using the right-hand grip rule, where one holds his hands as though he is gripping something with his thumb pointing in the direction of current flow, his fingers will curl in a way as to indicate the direction of the magnetic field. This is also the direction in which the needle deflects.

Types of Forces

• Static friction
  • Frictional force between surfaces at rest with respect to each other.
  • It increases with increasing applied force up to a maximum value (which is proportional to normal contact force).
• Kinetic friction
  • Frictional force acting between surfaces in relative motion.
• Viscous forces
  • Resistive force experienced by a solid moving in a fluid.
  • Dependent on speed of object v, e.g. $$F_D\propto v$$ at low speeds and $$F_D\propto v^2$$ at high speeds.

[accordions autoHeight='true'] [accordion title="1. Newton's Laws of Motion"]

• Newton's First Law:  a body will remain in its state of rest or uniform motion in a straight line unless acted upon by a resultant force.
• Newton's Second Law:  the rate of change of momentum of a body is proportional to the resultant force acting on it and the change takes place in the direction of the resultant force.
  • $$F =\frac{dp}{dt}$$ in general
  • $$F =ma$$ when mass is constant.
• Newton's Third Law:  if body A exerts a force on body B, then body B exerts an equal and opposite force on body A

[/accordion] [accordion title="2. Linear Momentum"]

• The linear momentum of a body is defined as the product of its mass and its velocity.
• Impulse is the product of the force acting on a body and the time interval during which the force is exerted. It is equal to the change in momentum of the body.
  • For constant force, impulse = $$\Delta p =F \Delta t$$
  • In general, impulse = $$\Delta p =\int {F .dt}$$

[/accordion] [accordion title="3. Collision Problems"]

• The principle of conservation of momentum states that the total momentum of a system of colliding objects remains constant provided no resultant external force acts on the system.
• Conservation of momentum applies to both elastic and inelastic collisions.
  • $$m_1u_1+m_2u_2=m_1v_1+m_2v_2$$
• Conservation of kinetic energy applies only to elastic collisions.
  • $$\frac{1}{2}m_1u_1^2+\frac{1}{2}m_2u_2^2=\frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2$$
• Relative speed of approach = Relative speed of separation
  • $$u_2-u_1=v_1-v_2$$

[/accordion] [/accordions]

[accordions autoHeight='true'] [accordion title="1. Definitions"]

• Displacement is the distance travelled along a specified direction.
• Speed is the rate of change of distance travelled.
• Velocity is the rate of change of displacement.
• Acceleration is the rate of change of velocity.

[/accordion] [accordion title="2. One-Dimensional Motion with Constant Acceleration"]

• $$v=u+at$$
• $$s=(\frac{u+v}{2})t$$
• $$s=ut+\frac{1}{2}at^2$$
• $$v^2=u^2+2as$$

s: displacement u: initial velocity v: final velocity a: acceleration t: time [/accordion] [accordion title="3. Two-Dimensional Motion"]

• Tip: Sometimes, you will require two equations to solve a kinematics problem. For a parabolic path in a projectile motion without resistive forces, you can draw a table such as the one below and fill in the blank with the information given in the question.

[caption id="attachment_1933" align="aligncenter" width="163"] Initial velocity at an angle[/caption]

• In the case where a projectile is launched at an angle $$\theta$$ to the horizontal and undergoes the acceleration of free fall, the various horizontal and vertical components of displacement, velocity and acceleration can be expressed in the following way:

	Horizontal	Vertical
displacement, s	$$(u \cos \theta)t$$	$$(u \sin \theta)t+\frac{1}{2}gt^2$$
initial velocity, u	$$u \cos \theta$$	$$u \sin \theta$$
initial velocity, v	$$u \cos \theta$$	$$u \sin \theta +gt$$
acceleration, a	0	$$g$$
time, t	same for	both dimensions

[/accordion] [/accordions]