Video Transcript
A car with mass 360 kilograms
travels at constant speed along a circular path around a flat roundabout. The radius of the roundabout is 12
meters. The car takes a time of 28 seconds
to completely travel around the roundabout. What is the friction force between
the wheels of the car and the surface of the road? Give your answer to the nearest
newton.
In this question, we have a car
traveling around a flat roundabout and would like to calculate the friction force
between the wheels of the car and the surface of the road.
Let’s begin by drawing out the
problem as follows. The car has a mass of 360
kilograms, which we’ve labeled as 𝑚, and the roundabout has a radius of 12 meters,
which we’ve labeled as 𝑟. When the car travels along the
roundabout, it will experience a force 𝐹 subscript c towards the center of the
roundabout. This force 𝐹 subscript c is known
as the centripetal force.
An important thing to note about
centripetal forces is that they always have physical causes for them. The reason that the car experiences
a centripetal force towards the center of the roundabout is due to the friction
between the car’s wheels and the surface of the road. Without this frictional force
acting on the car, it wouldn’t be able to follow this circular path.
Therefore, to calculate the
friction force between the wheels of the car and the surface of the road, we need to
calculate the centripetal force. Recall that the centripetal force
𝐹 subscript c on an object is given by the formula 𝐹 subscript c equals 𝑚 times
𝑟 times 𝜔 squared, where 𝑚 is the mass of the object, 𝑟 is the radius of the
circular path taken, and 𝜔 is the angular speed of the object. We already know that the car’s mass
is equal to 360 kilograms and the radius of the roundabout is equal to 12
meters. So now we need to calculate the
angular speed of the car.
We can recall that angular speed 𝜔
is defined as the rate of change of angular displacement. This can be represented as the
formula 𝜔 equals 𝛥𝜃 over 𝛥𝑡, where 𝛥𝜃 is the change in angular position and
𝛥𝑡 is the change in time. We are told in the question that
the car takes 28 seconds to completely travel around the roundabout. So 𝛥𝑡 is equal to 28 seconds. For a car to completely travel
around the roundabout, its change in angular position 𝛥𝜃 must be equal to two 𝜋
radians. Therefore, the car’s angular speed
𝜔 is equal to two 𝜋 radians divided by 28 seconds.
We can now substitute these values
for 𝑚, 𝑟, and 𝜔 into our formula for centripetal force. When we do this, we find that the
centripetal force 𝐹 subscript c is equal to 360 kilograms multiplied by 12 meters
multiplied by the square of two 𝜋 radians over 28 seconds. Completing this calculation gives a
result of 217.534 et cetera newtons. Rounding this to the nearest
newton, we find that the centripetal force is equal to 218 newtons.
Now, we noted earlier that this
centripetal force acting on the car is due to the frictional force between the
wheels of the car and the surface of the road. Therefore, the centripetal force
we’ve calculated is equal to the frictional force. So this 218 newtons that we’ve
calculated is the value of the friction force.
Our answer then is that the
friction force between the wheels of the car and the surface of the road is equal to
218 newtons.
