A car with its passengers have a total mass of 4200kg .the car is travelling along a horizontal road when it moves ,it experiences a forward driving force of magnitude F newtons and a constant resistance force(opposite to driving force)of 850N
a)what is the value of F if the car travels at a constant speed ?
b)find the value of F if the car accelecrates at 1.8 m/s2
c) if F =1800,find the acceleration of the car and describ what is happing to the speed of the car????
a) If the car travels at a constant speed, it means that the driving force is balanced by the resistance force. So, to calculate F, we need to equate the two forces:
F = 850 Newtons
b) If the car accelerates at 1.8 m/s², we need to calculate the total force acting on the car. The resistance force is still 850 N, but we need to find the additional driving force required to accelerate the car:
Total force = Resistance force + Driving force
Total force = 850 N + additional driving force
Using Newton's second law:
Total force = mass × acceleration
850 N + additional driving force = 4200 kg × 1.8 m/s²
Simplifying the equation, we can solve for the additional driving force:
additional driving force = (4200 kg × 1.8 m/s²) - 850 N
c) If F = 1800 N, we can use Newton's second law to calculate the acceleration of the car. Rearranging the formula for acceleration:
acceleration = Total force / mass
acceleration = (850 N + 1800 N) / 4200 kg
Describing what is happening to the speed of the car, if the acceleration is positive, it means the car is speeding up. If the acceleration is negative, it means the car is slowing down. If the acceleration is zero, it means the car is maintaining a constant speed.
a) If the car is traveling at a constant speed, it means the net force acting on the car is zero. The resistance force is opposing the driving force, so the driving force must be equal to the resistance force for the car to maintain a constant speed.
Therefore, F = 850 N.
b) When the car accelerates, we need to calculate the net force required to produce the given acceleration. We can use Newton's second law of motion:
net force = mass × acceleration
For the car to accelerate at 1.8 m/s^2, we plug in the values:
net force = 4200 kg × 1.8 m/s^2
net force = 7560 N
Since the resistance force is always opposing the driving force, we have:
net force = driving force - resistance force
Plugging in the given value for the resistance force:
7560 N = driving force - 850 N
Solving for the driving force, we find:
driving force = 7560 N + 850 N
driving force = 8410 N
So, the magnitude of the driving force is 8410 N.
c) If F = 1800 N, we can use the same equation as before to find the acceleration:
net force = driving force - resistance force
Plugging in the given values:
net force = 1800 N - 850 N
net force = 950 N
Now we can use Newton's second law to find the acceleration:
950 N = mass × acceleration
950 N = 4200 kg × acceleration
Solving for the acceleration, we find:
acceleration = 950 N / 4200 kg
acceleration ≈ 0.226 m/s^2
The positive acceleration indicates that the car is speeding up.
To answer these questions, we need to understand the concept of net force, which is the total force acting on an object. The net force determines the motion of the object. The net force is the vector sum of all the forces acting on the car.
Let's go through each question one by one:
a) In this case, the car is traveling at a constant speed. This implies that the net force acting on the car is zero because the car does not accelerate. So, to find the value of F, we need to consider the equilibrium condition.
The equilibrium condition states that the sum of all forces acting on an object is zero. Therefore, the driving force F must balance out the resistance force of 850 N in order to maintain a constant speed. Thus, F = 850 N.
b) In this case, the car is accelerating at a rate of 1.8 m/s^2. We can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration (F = m * a).
Here, the net force acting on the car is the difference between the driving force F and the resistance force of 850 N. So we can write the equation as follows:
F - 850 = m * a
To find the value of F, we can substitute the given values. The mass of the car is 4200 kg, and the acceleration is 1.8 m/s^2. Therefore:
F - 850 = 4200 * 1.8
Solving for F:
F = 4200 * 1.8 + 850
c) In this case, F = 1800 N is given, and we need to find the acceleration of the car. Using the same equation as in part b, we can rearrange it to solve for acceleration:
F - 850 = m * a
Substituting the given values:
1800 - 850 = 4200 * a
Solving for a:
950 = 4200 * a
a = 950 / 4200
Now, let's describe what is happening to the speed of the car. Since the driving force is greater than the resistance force, the net force on the car is nonzero, resulting in acceleration. The positive acceleration indicates an increase in speed. Thus, the car's speed is increasing.