Newtons Second Law- Grade 11 Physics

Question

A car of mass 1640kg is travelling at a speed of 25.0m/s when the brakes are applied. The car comes to a stop in a distance of 68.5m. How much force did the brakes exert on the car?

Answer 1

Hey Lauren,

The important thing to consider here before jumping into the mathematical portion is making sure we first understand what the relationship between force and motion. Forces cause motion which is the effect of all of the forces at play. This is what Newton’s 2nd law actually explains and is best represented as ∑F / mass = acceleration.

The next thing is to recognize that we can create a diagram that represents this scenario using arrows that represent all of the forces at play and each of those arrows is a vector quantity. This is referred to as a force diagram and any arrows that are unbalanced from each other (think 5+(-5)=0) will show you the direction of the acceleration due to the sum of forces as well. If you’d like an example of how to create a force diagram to help you solve any problem relating to Newtonian mechanics, feel free to message me and we can connect and find time for a session.

Now we can move to the quantitative portions where we know that the force should be opposite of the direction of the cars motion since the car is slowing which means the acceleration is negative instead of positive. Using our understanding of motion, or kinematics we can solve for the acceleration since we know the initial and final velocity as well as the distance the car travels which slowing to a stop. The only quantity we do not have besides the acceleration is the time interval which tells us we want to use a timeless mathematical relationship.

(V_f² - V_i²) / 2*Δx = a

once you have the acceleration you can solve for the sum of forces since you have the mass of the car as well. You can determine that the only force in the x direction should be the brakes causing the car to slow to a stop assuming that the friction of the tires on the road are also negligible.

ΣF / 1640kg = (0m/s² - 25.0m/s²) / 2*Δ68.5m = a

If you need anything further explained feel free to message me and we can find a chance to connect!

Answer 2

m=1640kg

v₀=25.0m/s

d=68.5m

v=0 m/s

d=v₀t-0.5*a*t²

(d-v₀t)=-0.5*a*t²

v=v₀-at

t=(25m/s)/a

Substitute back into (d-v₀t)=-0.5*a*t²

(d-v₀²/a)=-0.5*a*(v₀/a)²

da-v₀²=-0.5v₀²

da=0.5v₀²

a=0.5v₀²/d=(0.5)*(25m/s)²/68.5m=4.562m/s²

Newtons Second Law F=ma:

Breaking Force=m*a in direction opposite to the cars original traveling direction

Breaking Force=1640kg*4.562m/s²=7481.75 N (direction is in opposite direction to the cars original traveling directions)

Answer:

Breaking Force=7,481.75N (direction opposite to car direction of travel)

Simple Formula:

Force=(0.5*m*(v₀)²)/d