Question

Your go karts have a mass of 450kg and travel around a circular curve on a flat, horizontal track at a radius of 42 m.

a. The maximum frictional force between the tyres and the road is equal to 20% of the weight of the car and driver. Calculate the coefficient of friction when an adult of mass 70kg is driving the kart.


b. Calculate maximum angular velocity at which the car can travel round the curve at a constant radius of 42 m.

c. Calculate the maximum linear velocity.

d. You decide that this is not nearly fast enough and decide to create a banked track of 12O, what is the maximum linear velocity now?

e. It is important that the karts can brake effectively. They use drum brakes where a solid circular drum of mass 4.0 kg and radius 0.15 m is rotating at an angular speed of 22 rad s−1 about an axis when a ‘braking’ torque is applied to it which brings it to rest in 5.8 s.


can anyone please help on this? I think I've got an answer to a. as 0.02
I'm really struggling with b. onwards, can anyone explain b. especially, with steps please so I can understand?

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Answer 1

Explanation:

a. To calculate the coefficient of friction, we first need to determine the weight of the car and driver. The weight is given by the formula:

Weight = mass * gravitational acceleration

where the gravitational acceleration is approximately 9.8 m/s^2.

Weight = 70 kg * 9.8 m/s^2 = 686 N

Now, we can calculate the maximum frictional force using the given information:

Maximum frictional force = 20% * Weight = 0.2 * 686 N = 137.2 N

The frictional force is given by the formula:

Frictional force = coefficient of friction * Normal force

where the Normal force is equal to the weight of the car and driver. Therefore, we can rearrange the formula to solve for the coefficient of friction:

Coefficient of friction = Frictional force / Normal force

Coefficient of friction = 137.2 N / 686 N = 0.2

So, you are correct in your answer. The coefficient of friction is indeed 0.2.

b. To calculate the maximum angular velocity at which the car can travel around the curve, we can use the concept of centripetal force. The centripetal force is given by the formula:

Centripetal force = mass * (angular velocity)^2 * radius

In this case, the maximum centripetal force is provided by the maximum frictional force:

Centripetal force = Maximum frictional force = 137.2 N

Now we can substitute the given values into the equation:

137.2 N = 450 kg * (angular velocity)^2 * 42 m

Solving for the angular velocity:

(angular velocity)^2 = 137.2 N / (450 kg * 42 m)

angular velocity = sqrt(137.2 N / (450 kg * 42 m))

Calculating the value:

angular velocity ≈ 0.421 rad/s

So, the maximum angular velocity at which the car can travel around the curve is approximately 0.421 rad/s.

c. To calculate the maximum linear velocity, we can use the relationship between linear velocity and angular velocity:

Linear velocity = angular velocity * radius

Substituting the values:

Linear velocity = 0.421 rad/s * 42 m

Calculating the value:

Linear velocity ≈ 17.7 m/s

So, the maximum linear velocity is approximately 17.7 m/s.

d. When the track is banked at an angle of 120 degrees, we need to consider the effect of the banking on the maximum linear velocity. In this case, the centripetal force is provided by the horizontal component of the normal force, rather than the frictional force.

The vertical component of the normal force counteracts the weight of the car and driver:

Vertical component of normal force = Weight = 686 N

The horizontal component of the normal force provides the centripetal force:

Horizontal component of normal force = Weight * sin(banking angle)

Using the given banking angle of 120 degrees:

Horizontal component of normal force = 686 N * sin(120 degrees)

Calculating the value:

Horizontal component of normal force ≈ 596.1 N

Now, we can equate this force to the centripetal force:

Centripetal force = Horizontal component of normal force = 596.1 N

Using the same formula as before:

Centripetal force = mass * (angular velocity)^2 * radius

596.1 N = 450 kg * (angular velocity)^2 * 42 m

Solving for the angular velocity:

(angular velocity)^2 = 596.