Each of the four wheels of a car push on the road with a force of 4.0*10^3 N [down]. The driving force on the car is 8.0*10^3 N [W]. The fictional resistance on the car is 6.0*10^3 [E]. Calculate the following
A) the mass of the car
B) the net force on the car
C) the cars acceleration
The answers are
A) 1.6*10^3 kg
B) 2.0*10^3 N [W]
C) 1.2m/s^2
I just don't understand how to get these correct answers
M•g =4•m•g= 4•4•10^3 N
M = 4•4•10^3/9.8 =1.63•10^3 kg
There are 4 forces: Mg (downwards), normal force N ( upwards), driving force(to the left), and resistance force (to the right) . Net force is their sum.
Since N=Mg, net force is 8•10^3 – 6•10^3 = 2•10^3 N (to the left).
Acceleration = net force/mass =2•10^3/1.63•10^3 = 1.23 m/s^2
Well, let's break down the problem step by step and see how we can arrive at the correct answers using some clown humor along the way!
A) To find the mass of the car, we can start with the force of gravity acting on the car, which is equal to its weight. Since the car is on a level road, the weight of the car is equal to the force pushing down on the road by all four wheels combined. So, we divide the total downward force by the acceleration due to gravity (which is approximately 9.8 m/s^2):
Mass of the car = Total force / Acceleration due to gravity
That gives us:
Mass of the car = (4.0*10^3 N + 4.0*10^3 N + 4.0*10^3 N + 4.0*10^3 N) / 9.8 m/s^2
Now let's simplify this:
Mass of the car = 16.0*10^3 N / 9.8 m/s^2
And finally:
Mass of the car = 1.6*10^3 kg
B) The net force on the car can be found by subtracting the fictional resistance from the driving force:
Net force on the car = Driving force - Fictional resistance
That gives us:
Net force on the car = 8.0*10^3 N [W] - 6.0*10^3 N [E]
And after some funny calculations:
Net force on the car = 2.0*10^3 N [W]
C) The car's acceleration can be determined using Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration:
Net force on the car = Mass of the car * Acceleration
Rearrange the equation to solve for acceleration:
Acceleration = Net force on the car / Mass of the car
Plug in the values we found earlier:
Acceleration = 2.0*10^3 N [W] / 1.6*10^3 kg
And voila!
Acceleration = 1.2 m/s^2
I hope this clownish explanation helps clarify the steps to find the correct answers!
To solve these problems, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
A) To find the mass of the car, we can use the formula:
Net force = mass x acceleration
Rearranging the formula, we get:
Mass = Net force / acceleration
Given that the net force on the car is 8.0 * 10^3 N [W] and the acceleration is not provided, we cannot determine the mass of the car at this point. We would need the acceleration to proceed.
B) The net force on the car can be found by summing up the forces acting in the horizontal direction:
Net force = Driving force - Fictional resistance
Given that the driving force is 8.0 * 10^3 N [W] and the fictional resistance is 6.0 * 10^3 N [E], we can substitute these values into the formula:
Net force = 8.0 * 10^3 N [W] - 6.0 * 10^3 N [E]
Simplifying, we get:
Net force = 8.0 * 10^3 N [W] - (-6.0 * 10^3 N [W])
Net force = 8.0 * 10^3 N [W] + 6.0 * 10^3 N [W]
Net force = 14.0 * 10^3 N [W]
Net force = 1.4 * 10^4 N [W]
Therefore, the net force on the car is 1.4 * 10^4 N [W].
C) To find the car's acceleration, we can rearrange Newton's second law of motion:
Acceleration = Net force / mass
However, since we haven't determined the mass of the car, we cannot calculate the acceleration at this point.
To solve this problem, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
A) To find the mass of the car, we need to use the force equation and rearrange it to solve for mass. The driving force is given as 8.0*10^3 N [W], and the gravitational force exerted on the car is the weight, which can be calculated as the product of mass and acceleration due to gravity (9.8 m/s^2). Therefore, the weight is equal to (mass of the car) * (acceleration due to gravity).
Given the weight = 4.0*10^3 N [down], we can set up the equation as follows:
(mass of the car) * (9.8 m/s^2) = 4.0*10^3 N
Solving for the mass of the car, we have:
mass of the car = (4.0*10^3 N) / (9.8 m/s^2) = 1.6*10^3 kg
So, the mass of the car is 1.6*10^3 kg.
B) The net force on the car can be calculated by adding up all the forces acting on it. In this case, we have the driving force of 8.0*10^3 N [W] pushing the car forward, and the fictional resistance of 6.0*10^3 N [E] opposing its motion. Since the forces are in opposite directions, we need to subtract the resistance force from the driving force to get the net force.
Net force = driving force - resistance force
= 8.0*10^3 N [W] - 6.0*10^3 N [E]
= 2.0*10^3 N [W]
Therefore, the net force on the car is 2.0*10^3 N [W].
C) To find the car's acceleration, we can rearrange the force equation from Newton's second law:
(mass of the car) * (acceleration) = (net force)
Given the mass of the car as 1.6*10^3 kg and the net force as 2.0*10^3 N [W], we can solve for acceleration:
(1.6*10^3 kg) * (acceleration) = 2.0*10^3 N
Simplifying the equation gives us:
acceleration = (2.0*10^3 N) / (1.6*10^3 kg)
= 1.2 m/s^2
Therefore, the car's acceleration is 1.2 m/s^2.