Exam Revision

Linear Motion

Distinguish between scalar and vector quantities, and add and subtract vectors in one dimension

• Scalar quantities have a magnitude, Vectors have both direction and magnitude
  • Scalar - distance, e.g. $4.57m$
  • Vector - displacement, e.g. $4.57m \space South$
• Adding and subtracting is as it is in maths.
  • Subtract the negative e.g. *What is the change in velocity of Bongleshnout's Scooter as he turns a corner if he approaches it at $18.7ms^{-1}$ west and exits it at $16.6ms^{-1}$ north?
    • Remember: $\Delta v=v_{f}-v_{i}=v_f+(-v_i)$
    • As such, this would be $16.6ms^{-1}$ north + $18.7ms^{-1}$ east
    • Work from there.

Uniformly accelerated motion is described in terms of relationships between measurable scalar and vector quantities, including displacement, speed, velocity and acceleration —this includes applying SUVAT

• The quantities:
  • Displacement is a vector $m$
  • Speed is a scalar $m \space s ^{-1}$
  • Velocity is a vector $m \space s ^{-1}$
  • Acceleration is a vector $m \space s ^{-2}$
• Remember, simultaneous may have to be done between the SUVATs

Representations, including graphs, vectors, and equations of motion, can be used qualitatively and quantitatively to describe and predict linear motion

• N.B. m/s to km/h is multiplication by 3.6, and vice versa.

Graphs

• Velocity-Time
  • Derivative is acceleration
  • Integral is displacement
• Acceleration-Time
  • Derivative is **JERK
  • Integral is change in velocity

Equations

• When considering maximum height problems, there will exist a velocity $0$
• On inclined planes, use the equation $g \space \sin(\theta)$
  • Remember, mass has no impact on acceleration (though it does on friction, but on inclined plane questions friction is usually discounted)

Vertical motion is analysed by assuming the acceleration due to gravity is constant near Earth’s surface

• The value $a$ for gravity is $9.8m \space s^{-2}$

Newton’s three Laws of Motion describe the relationship between the force or forces acting on an object, modelled as a point mass, and the motion of the object due to the application of the force or forces

• Force ($F$) is measured in $N$; it is a vector quantity
• Laws
  1. An object will maintain constant velocity unless an unbalanced, external force acts on it - informally, 'no force, no acceleration'
     • Inertia is considered to be the resistance to a change in motion of an object.
     • It is directly related to momentum.
     • Due to inertia, an object will continue with its motion unless a net force acts on the object.
  2. $F=ma$
     • i.e. 'The acceleration of an object is directly proportional to the net force on the object and inversely proportional to the mass of the object'
     • $F=ma, \space \therefore F=\frac{\Delta p}{\Delta t}$
  3. For every action (force), there is an equal and opposite reaction (force).

Free body diagrams show the forces and net force acting on objects, from descriptions of real-life situations involving forces acting in one or two dimensions

• This is an experience thing, just know how to do it.

Momentum is a property of moving objects; it is conserved in a closed system and may be transferred from one object to another when a force acts over a time interval

• Momentum is conserved in a closed system and a property of moving objects. It is a vector quantity
• $p=mv$
  • mass x velocity
  • measured by $kg \space m\space s^{-1}$
• Momentum is conserved in interactions between objects and thus $\sum\limits P$ before = $\sum\limits P$ after.
  • Since it involves many vectors, to get direction easily, assign a negative and a positive.
• Change in momentum is impulse
  • $=mv-mu=m(v-u)=m\Delta v$
  • Unit is $N s$ (Newton-Seconds) and is a **vector

Energy is conserved in isolated systems and is transferred from one object to another when a force is applied over a distance; this causes work to be done and changes the kinetic (Ek) and/or potential (Ep) energy of objects

• Energy is the capacity to cause a change
• Kinetic and Potential energy are both types of Mechanical energy, measures in Joules as a Scalar
  • Any moving object has kinetic energy.
    • $=\frac{1}{2}mv^2$
  • Potential energy is the energy of objects relative to one another or in fields.
    • Gravitational potential Energy (GPE) is $mgh$
• Work is the transferring or transforming of energy on an object.
  • $W=Fs$ or $W=Fs\cos \theta$ where $\theta$ is the angle between $F$ and $s$
    • or $=\frac{1}{2}mv^2-\frac{1}{2}mu^2$
  • It is measured in Joules as a Scalar
  • If a force is applied on an object but it does not move ($s=0$), then no work is done on it.
  • On a force-displacement graph, work is the integral.
• Total Mechanical Energy is the sum of kinetic and GPE energies

Collisions may be elastic and inelastic; kinetic energy is conserved in elastic collisions

• Literally what the objective says.

Power is the rate of doing work or transferring energy

• Measures in Watts as a Scalar

Car Crashes

Seatbelts

• Due to Newton's first law, if a car suddenly decelerates, then the occupants will stay in motion, flying out the window or hitting it (bad). Seatbelts oppose the inertia of occupants' bodies.

Airbag

• As the occupants move forward due to inertia, airbags increase the time that the force is applied. Due to this, impulse is drawn out over a greater period of time and force is minimized.

Crumple zones, helmets and safety barriers

• Same as airbags. Increase time, decreasing force.

Waves

Questions

(from pearson)

1. Determine the resultant force when forces of $5.0N$ east and $3.0N$ north act on a tree.
2. Determine the change in velocity of a ball as it bounces off a wall. The ball approaches at $7.0m\space s^{-1}$ south and rebounds at $6.0m \space s^{-1}$ east. Make sure to include an appropriate vector diagram.
3. Bob is applying a force of $15.0N$ to a sled on a frictionless surface, using a handle that is angled $50\degree$ to the ground. The sled weighs $7.45kg$. What is its acceleration?
4. A golf ball is dropped onto a concrete floor and strikes the floor at $9.0m \space s^{-1}$. It then rebounds at $7.00m \space s^{-1}$. The contact time with the floor is $35ms$. What is the average acceleration of the ball during its contact with the floor?
5. A cyclist takes $4.00s$ to slow down at $-3.00m \space s^{-2}$ and completely stop. Calculate the initial velocity of the cyclist.
6. A $1200kg$ wrecking ball is moving at $2.50m \space s^{-1}$ north towards a $1500kg$ wrecking ball moving at $4.00m \space s^{-1}$ south. Calculate the final velocity of the more massive wrecking ball if the other ball rebounds at $3.50m \space s^{-1}$ south.
7. A $65.0g$ pool ball is moving at $0.250m \space s^{-1}$ south towards a cushion and bounces off at $0.200 m \space s^{-1}$ east. Calculate the impulse on the ball during the change in velocity.
8. Calculate the final velocity of a $307g$ fish that accelerates for $5.20s$ from rest due to a force of $0.250N$ left.
9. A student drops a $56.0g$ egg onto a table from a height of $60 cm$. Just before it hits the table, the velocity of the egg is $3.43m\space s^{−1}$ down. The egg’s final velocity is zero as it smashes on the table. The time it takes for the egg to change its velocity to zero is $3.55ms$.
10. A car with a mass of $1200kg$ is travelling at $90km\space h^{−1}$. Calculate its kinetic energy at this speed.
11. As a bus with a mass of $10$ tonnes approaches a school it slows from $60km\space h^{−1}$ to $40km\space h^{−1}$. Calculate, to 2 sig figs, the work done by the brakes on the bus and the average force applied by the truck's brakes if it travels $40m$ over deceleration.
12. A $200g$ snooker ball with initial velocity $9.0m\space s^{−1}$ to the right collides with a stationary snooker ball of mass $100g$. After the collision, both balls are moving to the right and the $200g$ ball has a speed of $3.0m\space s^{−1}$. Show calculations to test whether or not the collision is inelastic.
13. A father picks up his baby from its bed. The baby has a mass of $6.0kg$ and the mattress of the bed is $70cm$ above the ground. When the father holds the baby in his arms, it is $125cm$ off the ground. Calculate the increase in gravitational potential energy of the baby, taking $g$ as $9.80N\space kg^{−1}$ and giving your answer correct to two signifcant fgures.
14. An arrow with a mass of $35g$ is fired into the air at $80m\space s^{−1}$ from a height of $1.4m$. Calculate the speed of the arrow when it has reached a height of $30m$.
15. An $800.0kg$ racecar’s engine is capable of generating $120kW$ of power. How long does it take the car to accelerate from $40.0m\space s^{−1}$ to $55.0m\space s^{−1}$?