3.16. An 1100-kg car accelerates from 0 to 30 m/sec in 12 sec. If a frictional force of 200 N opposes the motion, what forces must the wheels exert backward on the pavement to cause this acceleration?
a = 30/12 = 2.5 m/s^2
F-200 = m a = 1100(2.5) =2750 N
F = 2950 N
To determine the forces exerted by the wheels on the pavement, we need to consider Newton's second law of motion, which states that the net force on an object is equal to the mass of the object multiplied by its acceleration.
The net force acting on the car can be calculated using the equation:
Net force = Mass × Acceleration
Given that the mass of the car is 1100 kg and the acceleration is (30 m/s - 0 m/s) / 12 s = 2.5 m/s^2, we can substitute these values into the equation:
Net force = 1100 kg × 2.5 m/s^2
= 2750 N
Now we need to take into account the frictional force opposing the motion, which is 200 N. The frictional force acts in the opposite direction to the acceleration. Therefore, the net force acting on the car is the sum of the applied force and the frictional force:
Net force = Applied force - Frictional force
Substituting the known values, we can rewrite the equation as:
2750 N = Applied force - 200 N
To isolate the applied force, we can rearrange the equation:
Applied force = 2750 N + 200 N
= 2950 N
Therefore, the force that the wheels must exert backward on the pavement to cause this acceleration is 2950 Newtons.
To find the forces that the wheels exert backward on the pavement, we first need to calculate the net force acting on the car.
1. Calculate the acceleration:
The equation to calculate acceleration is:
acceleration = change in velocity / time
In this case,
Initial velocity (u) = 0 m/sec
Final velocity (v) = 30 m/sec
Time (t) = 12 sec
acceleration = (v - u) / t
acceleration = (30 - 0) / 12
acceleration = 30 / 12
acceleration = 2.5 m/sec²
2. Calculate the net force:
The net force acting on an object is given by Newton's second law of motion:
net force = mass × acceleration
In this case,
Mass (m) = 1100 kg
Acceleration (a) = 2.5 m/sec²
net force = mass × acceleration
net force = 1100 kg × 2.5 m/sec²
net force = 2750 N
3. Calculate the force exerted by friction:
The frictional force opposes the motion, so it acts in the opposite direction. Its magnitude is given as 200 N.
4. Calculate the force exerted by the wheels:
The force exerted by the wheels must counteract both the net force and the frictional force. Since they act in opposite directions, the force exerted by the wheels can be calculated by adding the magnitudes of the two forces.
Force exerted by the wheels = net force + frictional force
Force exerted by the wheels = 2750 N + 200 N
Force exerted by the wheels = 2950 N
Therefore, the wheels must exert a force of 2950 N backward on the pavement to cause this acceleration.