A book resting on a table is an example of balanced forces
A tug-of-war is an example of when forces can become unbalanced
F = m × a
A car salesman says that his best car has a mass of 900 kg and can accelerate from 0 to 27 m/s in 3 seconds.Calculate:
a) The acceleration of the car in the first 3 seconds.
b) The force required to produce this acceleration.
Part (a)
Step 1: List the known quantities
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
Step 2: Identify which law of motion to apply
F = ma
Step 3: Calculate the force required to accelerate the car
F = 900 × 9 = 8100 N
A passenger of mass 70 kg travels in a car at a speed of 20 m/s.The vehicle is involved in a collision, which brings the car (and the passenger) to a halt in 0.1 seconds.Calculate:
a) The deceleration of the car (and the passenger).
b) The decelerating force on the passenger.
Part (a)
Step 1: List the known quantities
Step 2: Calculate the change in velocity of the car (and the passenger)
change in velocity = Δv = final velocity − initial velocity = v − u
Δv = 0 − 20
Δv = −20 m/s
Step 3: Calculate the deceleration 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: List the known quantities
Step 2: State the relationship between resultant force, mass and acceleration
F = m × a
Step 3: Calculate the decelerating force
F = 70 × −200
F = −14 000 N
Remember that resultant force is a vector quantityExaminers may ask you to comment on why its value is negative - this happens when the resultant force acts in the opposite direction to the object's motionIn the worked example above, the resultant force opposes the passenger's motion, slowing them down (decelerating them) to a halt, this is why it has a minus symbol.
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