5.7.2牛顿第二定律

• Newton'ssecond law of motionstates:

The acceleration of an object is proportional to the resultant force acting on it and inversely proportional to the object's mass

• Newton's second law explains the following important principles:
  • An object willaccelerate(change its velocity) in response to aresultant force
  • Thebiggerthis resultant force, thelargerthe acceleration
  • For a given force, thegreaterthe object's mass, thesmallerthe acceleration experienced

• The image below shows some examples of Newton's second law in action:

Objects like baseballs and lawnmowers accelerate when a resultant force is applied on them. The size of the acceleration is proportional to the size of the resultant force

• Newton's second law can be expressed as an equation:

F=ma

• Where:
  • F= resultant force on the object in Newtons (N)
  • m= mass of the object in kilograms (kg)
  • a= acceleration of the object in metres per second squared (m/s²)

• This equation can be rearranged with the help of a formula triangle:

Force, mass, acceleration formula triangle

Part (a)

Step 1: List the known quantities

• • Initial velocity = 0 m/s
  • Final velocity = 27 m/s
  • Time,t= 3 s

Step 2: Calculate the change in velocity

change in velocity = Δv= final velocity − initial velocity

Δv= 27 − 0 = 27 m/s

Step 3: State the equation for acceleration

Step 4: Calculate the acceleration

a = 27 ÷ 3 =9 m/s²

Part (b)

Step 1: List the known quantities

• • Mass of the car,m= 900 kg
  • Acceleration,a= 9 m/s²

Step 2: Identify which law of motion to apply

• • The question involves quantities offorce,massandacceleration, so Newton's second law is required:

F=ma

Step 3: Calculate the force required to accelerate the car

F= 900 × 9 =8100 N

Step 1: Identify which law of motion to apply

• • The question involves quantities offorceandacceleration, and the image shows trolleys of differentmasses, soNewton's second lawis required:

F=ma

Step 2: Re-arrange the equation to make acceleration the subject

Step 3: Explain the inverse proportionality between acceleration and mass

• • Acceleration isinversely proportionalto mass
  • This means for thesame amount of force, alargemasswill experience asmallacceleration
  • Therefore, trolleyCwill have the smallest acceleration because it has the largest mass

• Newton's second law can be used toestimatethe sizes offorcesandaccelerationsin realistic scenarios
• When estimating quantities, an approximate answer can be shown using the symbol ~
  • For example, an adult person has a mass of ~70 kg

Part (a)

Step 1: Estimate the required quantities and list the known quantities

A moderate speed for a car is about 50 mph or 20 m/s

• • Initial velocity ~ 20 m/s
  • Final velocity = 0 m/s
  • Time,t= 0.1 s

Step 2: Calculate the change in velocity of the car (and the passenger)

change in velocity = Δv= final velocity − initial velocity

Δv= 0 − 20

Δv= −20 m/s

Step 3: Calculate the acceleration of the car (and the passenger) using the equation:

Step 4: Calculate the deceleration

a= −20 ÷ 0.1

a~−200 m/s²

Part (b)

Step 1: Estimate the required quantities and list the known quantities

An adult person has a mass of about 70 kg

• • Mass of the passenger,m~ 70 kg
  • Acceleration,a= −200 m/s²

Step 2: State Newton's second law

• • This question involves quantities of force, mass and acceleration, so the equation for Newton's second law is:

F=ma

Step 3: Calculate an estimate for the decelerating force

F= 70 × −200

F~−14 000 N