The mass of a sports car is 1100 kg. The shape of the car is such that the aerodynamic drag coefficient is 0.240 and the frontal area is 2.40 m2. Neglecting all other sources of friction, calculate the initial acceleration of the car ,if it has been traveling at 105 km/h and is now shifted into neutral and is allowed to coast. (Take the density of air to be 1.295 kg/m2.)
To calculate the initial acceleration of the car when it is shifted into neutral and allowed to coast, we need to first calculate the drag force acting on the car. The drag force can be calculated using the formula:
Drag Force = 0.5 * Cd * A * ρ * V^2
Where:
Cd is the drag coefficient (0.240)
A is the frontal area of the car (2.40 m^2)
ρ is the density of air (1.295 kg/m^3)
V is the velocity of the car (105 km/h)
First, convert the velocity from km/h to m/s:
105 km/h = (105 * 1000) / 3600 m/s ≈ 29.167 m/s
Now, substitute the given values into the drag force formula:
Drag Force = 0.5 * 0.240 * 2.40 * 1.295 * (29.167)^2
Simplifying the equation gives us:
Drag Force ≈ 7.646 N
Next, we need to calculate the net force acting on the car. Since the car is coasting and no external forces are acting on it (such as the engine or brakes), the net force is equal to the drag force.
Net Force = Drag Force ≈ 7.646 N
Finally, we can use Newton's second law of motion to calculate the acceleration of the car:
Net Force = mass * acceleration
Rearranging the formula and substituting the values, we get:
acceleration = Net Force / mass = 7.646 N / 1100 kg ≈ 0.0070 m/s^2
Therefore, the initial acceleration of the car when it is shifted into neutral and allowed to coast is approximately 0.0070 m/s^2.