a car of mass 1200 kg starts from rest, accelerates uniformly to a speed 4ms-1 in 2 seconds and continues moving at this constant speed in a horizontal straight line for additional 10s.
the brakes are then applied and the car is brought to rest in 4s. a constant resistance force of 500 N is acting on the car during its entire motion.
a) calculate the force accelerating the car in first 2 sec of the motion
b) calculate the average power developed by the engine in the first 2 sec of the motion
c) calculate the force pushing the car forward in the next 10 sec
d) calculate the power developed by the engine in those 10 sec
e) calculate the braking force in the last 4s of the motion
f) describe the energy transformations that have taken place in the 16s of the motion of the car.
please, i need it in 3 hours
a) calculating the force accelerating the car in the first 2 seconds of motion:
Given:
Mass of the car, m = 1200 kg
Initial velocity, u = 0 (as the car starts from rest)
Final velocity, v = 4 m/s
Time, t = 2 seconds
Using the equation of motion:
v = u + at
We can rearrange this equation to solve for acceleration (a):
a = (v - u) / t
Plugging in the values:
a = (4 - 0) / 2
a = 2 m/s²
The force accelerating the car can be calculated using Newton's second law:
Force = mass x acceleration
Force = 1200 kg x 2 m/s²
Force = 2400 N
Therefore, the force accelerating the car in the first 2 seconds is 2400 N.
b) calculating the average power developed by the engine in the first 2 seconds of motion:
Power is defined as the rate at which work is done. In this case, work is done by the engine in accelerating the car.
The equation for power is:
Power = Work / Time
The work done on the car can be calculated using the equation:
Work = Force x Distance
In the first 2 seconds, the car starts from rest and reaches a final velocity of 4 m/s. The average velocity during this time is (0 + 4) / 2 = 2 m/s.
The distance covered can be calculated using the equation:
Distance = Average Velocity x Time
Distance = 2 m/s x 2 s
Distance = 4 m
Plugging in the values:
Work = 2400 N x 4 m
Work = 9600 J
Now, we can calculate the average power:
Power = Work / Time
Power = 9600 J / 2 s
Power = 4800 W
Therefore, the average power developed by the engine in the first 2 seconds is 4800 W (Watts).
c) calculating the force pushing the car forward in the next 10 seconds:
During the next 10 seconds, the car moves at a constant speed of 4 m/s. Therefore, there is no acceleration.
The constant resistance force of 500 N is acting on the car.
Since the car is moving at a constant speed, the net force acting on it must be zero. Therefore, the force pushing the car forward is equal to the resistance force:
Force = 500 N
Therefore, the force pushing the car forward in the next 10 seconds is 500 N.
d) calculating the power developed by the engine in those 10 seconds:
During this time, the car is moving at a constant speed, so there is no acceleration and no additional work done by the engine.
The power developed by the engine can be calculated using the formula:
Power = Force x Velocity
Plugging in the values:
Power = 500 N x 4 m/s
Power = 2000 W
Therefore, the power developed by the engine in those 10 seconds is 2000 W (Watts).
e) calculating the braking force in the last 4 seconds of motion:
To calculate the braking force, we'll consider the deceleration of the car when the brakes are applied.
Given:
Time, t = 4 seconds
Final velocity, v = 0 (as the car is brought to rest)
Initial velocity, u = 4 m/s
Using the equation of motion:
v = u + at
Rearranging the equation to solve for acceleration (a):
a = (v - u) / t
Plugging in the values:
a = (0 - 4) / 4
a = -1 m/s²
The negative sign indicates deceleration.
The force can be calculated using Newton's second law:
Force = mass x acceleration
Force = 1200 kg x (-1 m/s²)
Force = -1200 N
Therefore, the braking force in the last 4 seconds of motion is 1200 N in the opposite direction.
f) describing the energy transformations that have taken place in the 16 seconds of the motion of the car:
During the 16 seconds of motion, the car goes through the following energy transformations:
1. Initially, the car has potential energy due to gravity but no kinetic energy as it starts from rest.
2. As the car accelerates uniformly in the first 2 seconds, energy is transferred from the engine (in the form of work done) to the car, increasing its kinetic energy.
3. During the next 10 seconds, the car is moving at a constant speed, so the energy is conserved. The engine is providing just enough power to counteract the resistance force, so there is no change in the car's kinetic energy.
4. When the brakes are applied, the car slows down, and its kinetic energy decreases. The energy is transferred to the braking system, resulting in thermal energy (due to friction) and potential energy (if the braking system involves raising a weight, for example).
5. Finally, when the car comes to rest, all its kinetic energy is converted into other forms of energy like potential energy (if the car is on an inclined surface), thermal energy (due to braking friction), and sound energy (due to braking noise).
Throughout the motion, there is some energy loss due to the resistance force acting against the motion of the car, resulting in some dissipated energy in the form of heat (due to friction) and sound energy.
Note: These energy transformations are simplified assumptions and do not account for all possible factors, such as air resistance or other losses in the system.
To solve this problem, we need to apply Newton's second law of motion and the work-energy principle.
a) The force accelerating the car in the first 2 seconds can be determined using Newton's second law, which states that force (F) equals mass (m) times acceleration (a). In this case, the car starts from rest and reaches a final speed of 4 m/s in 2 seconds, so the acceleration can be calculated as follows:
acceleration (a) = (final velocity - initial velocity) / time
= (4 m/s - 0 m/s) / 2 s
= 2 m/s^2
Now we can calculate the force accelerating the car:
force (F) = mass (m) * acceleration (a)
= 1200 kg * 2 m/s^2
= 2400 N
Therefore, the force accelerating the car in the first 2 seconds is 2400 N.
b) The average power developed by the engine in the first 2 seconds can be calculated using the work-energy principle. The work done by the engine is equal to the change in kinetic energy. The initial kinetic energy is zero as the car starts from rest, and the final kinetic energy is given by:
kinetic energy (KE) = (1/2) * mass (m) * final velocity^2
= (1/2) * 1200 kg * (4 m/s)^2
= 9600 J
The work done by the engine is:
work (W) = kinetic energy (KE) - initial kinetic energy
= 9600 J - 0 J
= 9600 J
The time taken is 2 seconds, so the average power developed by the engine is given by:
average power = work / time
= 9600 J / 2 s
= 4800 W (or 4.8 kW)
Therefore, the average power developed by the engine in the first 2 seconds is 4800 W.
c) The force pushing the car forward in the next 10 seconds is equal to the constant resistance force acting on the car, which is 500 N.
Therefore, the force pushing the car forward in the next 10 seconds is 500 N.
d) The power developed by the engine in the next 10 seconds can be calculated by finding the work done by the engine during this time period. Since the car is moving at a constant speed, the net work done is zero. This means that the power developed by the engine is also zero.
Therefore, the power developed by the engine in the next 10 seconds is 0 W.
e) To calculate the braking force in the last 4 seconds, we can use the work-energy principle again. The initial kinetic energy is given by:
kinetic energy (KE) = (1/2) * mass (m) * initial velocity^2
= (1/2) * 1200 kg * (4 m/s)^2
= 9600 J
The final kinetic energy is zero as the car comes to rest. The work done by the brake force is:
work (W) = kinetic energy (KE) - final kinetic energy
= 9600 J - 0 J
= 9600 J
The time taken is 4 seconds, so the braking force can be calculated as:
braking force = work / distance
= work / (mass * acceleration)
= 9600 J / (1200 kg * (4 m/s^2))
= 2.5 N
Therefore, the braking force in the last 4 seconds is 2.5 N.
f) The energy transformations that have taken place in the 16 seconds of the motion of the car are as follows:
1. Initially, the car has no kinetic energy but potential energy due to its position relative to the ground.
2. As the car accelerates uniformly, the potential energy is converted into kinetic energy.
3. The engine does work on the car, converting some chemical energy into kinetic energy.
4. When the car reaches a constant speed and moves horizontally, there is no change in kinetic energy, and the engine is not doing work.
5. During the next 10 seconds, the car continues to move at a constant speed, so no additional energy transformations occur.
6. When the brakes are applied, the kinetic energy of the car is gradually decreased, and the mechanical energy is dissipated as heat through the braking force.
7. Finally, when the car comes to rest, it has no kinetic energy, and the energy is fully dissipated as heat due to the brake force.
Thus, the energy transformations that have taken place in the 16 seconds of the car's motion involve the conversion of potential energy to kinetic energy, the work done by the engine, the dissipation of energy as heat through the braking force, and the conversion of kinetic energy to potential energy as the car comes to rest.
a) force=ma
b)power=force*distance/time=ma*1/2 a t
c)constant speed: force=500N
d) you do these, I can check you, all are pretty straightforwrd