Higher Advanced Mathematics of Mechanics SQA
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26 topics in 3 modules
☑️ Forces, Energy and Momentum 9 topics
- Applying impulse, change in momentum and conservation of momentum
- Determining and applying work done by a constant or variable force
- Using the concepts of kinetic and potential energy
- Applying the work–energy principle
- Applying the principle of the conservation of energy
- Determining the turning effect of force
- Using moments to find the centre of mass of a body
- Using Newton’s First and Third laws of motion to understand equilibrium
- Using the concepts of static friction and limiting friction on bodies in equilibrium
☑️ Straight Line, Periodic and Parabolic Motion 5 topics
- Applying graphs, calculus and equations of motion in one dimension to problems involving displacement, velocity and acceleration
- Applying displacement, velocity and acceleration vectors to resultant and relative motion
- Applying Newton’s Second Law of motion
- Applying equations to motion in horizontal and vertical circles with uniform angular velocity
- Applying the concept of simple harmonic motion (SHM)
☑️ Mathematical Techniques for Mechanics 12 topics
- Decomposing a rational function into a sum of partial fractions
- Differentiating, exponential, natural logarithmic, and trigonometric functions
- Differentiating functions using the chain rule, and functions given in the form of a product and in the form of a quotient
- Finding the derivative where relationships are defined implicitly or parametrically
- Integrating expressions using standard results
- Integrating using a substitution
- Integrating by parts
- Applying integration to a range of physical situations
- Solving a first-order linear differential equation with variables separable
- Solving a first-order linear differential equation using an integrating factor
- Solving a second-order homogeneous differential equation
- Applying mathematical techniques to problems
Higher Advanced Mathematics of Mechanics SQA Revision Content
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Higher Advanced Mathematics of Mechanics SQA - Forces, Energy and Momentum - Applying impulse, change in momentum and conservation of momentum Content Preview
Forces, Energy and Momentum
Applying impulse, change in momentum and conservation of momentum
Impulse and Change in Momentum
- Impulse is defined as force times time: it is the product of the average force exerted on an object and the time interval over which the force acts.
- In mathematical terms, impulse is also defined as the change in momentum of an object when a force is applied.
- Momentum is a vector quantity as it has direction as well as magnitude.
- In physics, momentum is usually denoted by the letter 'p', and it is calculated by multiplying the mass of an object (m) by its velocity (v). Therefore, p=mv.
- Momentum is conserved in a closed system where external forces are not at play. This is known as the conservation of momentum.
Applying the Concept of Impulse and Change in Momentum
- The concept of impulse can be applied to understand how the velocity of an object changes when a force is applied.
- For example, when a football is kicked, the shoe applies a force to the football over a short period of time. This force changes the football’s velocity, and hence its momentum.
- The greater the impulse, the greater the change in momentum. If the force is applied for a longer period of time, the change in the object’s momentum will be more significant.
- In an impact between two objects, the total momentum before the impact is equal to the total momentum after the impact (assuming no external forces are at work). This concept is central to the principle of conservation of momentum.
Conservation of Momentum
- The principle of conservation of momentum states that in a closed system, the total linear momentum of the system remains constant if no external forces act on it.
- In a collision, the total momentum of the colliding objects is the same before and after the collision.
- Therefore, if you have two objects, their combined momentum before the collision equals their combined momentum after the collision.
- This principle has significant practical applications in real-world physics including, for example, the study of vehicle collisions or the performance of rocket propulsion systems.
Question: A cricket ball of mass 0.15kg is hit by a bat, causing its velocity to change from 10m/s to 40m/s in the opposite direction, calculate the impulse exerted on the cricket ball.
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