A car of mass 1200kg accelerates from rest to a speed of 8.0ms in a time of 2.0s.
a)calc the forward driving force acting on the car while it is accelerating.
b)At high speeds the resistive frictional force F produced by the air on a body moving with velocity V is given by the equation F=bv^2 where b is a constant.
i)Derive the base units of force in the SI system.
ii)Determine the base units of b in the SI system.
iii)The car continues with the same forward driving force and accelerates until it reaches a top speed of 50ms.At the speed the resistive force is given by the equation F=bv^2.Determine the value of b for the car.
a) First calculate the acceleration a=(8-0)/2,0=4ms^-2
therefore force (F)=m*a=1200*4
=4800newtons
does anyone know the "b" and the following questions?
if you do please answer now
a) To calculate the forward driving force acting on the car while it is accelerating, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a).
Given:
Mass (m) = 1200 kg
Acceleration (a) = (final velocity - initial velocity) / time
Initial velocity (u) = 0 m/s
Final velocity (v) = 8.0 m/s
Time (t) = 2.0 s
First, calculate the acceleration:
a = (v - u) / t
a = (8.0 m/s - 0 m/s) / 2.0 s
a = 4.0 m/s^2
Next, calculate the forward driving force:
F = m * a
F = 1200 kg * 4.0 m/s^2
F = 4800 N
Therefore, the forward driving force acting on the car while it is accelerating is 4800 N.
b) i) To derive the base units of force in the SI system, we can use the equation F = m * a, where F is force, m is mass, and a is acceleration.
The SI units for mass (m) is kilograms (kg), and the SI units for acceleration (a) is meters per second squared (m/s^2).
Therefore, the base unit of force in the SI system is kilograms multiplied by meters per second squared (kg * m/s^2), commonly known as the Newton (N).
b) ii) To determine the base units of b in the SI system, we can use the given equation F = b * v^2, where F is force, b is a constant, and v is velocity.
Comparing the equation to the SI unit of force (N = kg * m/s^2), we can determine the units of b:
F = b * v^2
N = b * (m/s)^2
kg * m/s^2 = b * (m/s)^2
By comparing the units, we can see that b is dimensionless. It does not have any units.
b) iii) To determine the value of b for the car, we need to use the equation F = b * v^2, where F is force, b is the constant we need to find, and v is velocity.
At the top speed of 50 m/s, the resistive force is given by the equation F = b * v^2.
Let's assume that the resistive force (F) at this speed is known. If we can gather that information, we can directly calculate b.
Please provide the value for F, and we can use it to determine the value of b.
a) To calculate the forward driving force acting on the car while it is accelerating, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) times acceleration (a). So the formula to calculate force is:
F = ma
We are given:
Mass (m) = 1200 kg
Acceleration (a) = (final velocity - initial velocity) / time = (8.0 m/s - 0 m/s) / 2.0 s = 4.0 m/s^2
Plugging in these values into the formula, we get:
F = 1200 kg * 4.0 m/s^2 = 4800 N
Therefore, the forward driving force acting on the car while it is accelerating is 4800 Newtons.
b) ii) To determine the base units of b in the SI system, we need to examine the given equation: F = bv^2. Since force (F) is given in Newtons (N) and velocity (v) is given in meters per second (m/s), we can deduce the units of the constant b.
F = b * v^2
Newton = (b) * (m/s)^2
The units for velocity (m/s) are derived from the base units of length (meter, m) divided by the base unit of time (second, s). Square both sides of the equation:
1 N = b * (m^2/s^2)
Now we can identify the base units of b as Newton multiplied by inverse meters squared, per square second (N * m^(-2) * s^(-2)).
iii) To determine the value of b for the car at a top speed of 50 m/s, we can set up an equation using the given resistive force equation: F = bv^2. Rearranging the equation, we get:
b = F / v^2
Since we are given the top speed (v) as 50 m/s and we know that the forward driving force remains the same, we can calculate the value of b. However, we do not have the exact value of F at the top speed given in the question. Without that information, we cannot determine the specific value of b.