an automobile having a mass of 1.250 kg is traveling at 40m/s. what is its energy in kJ? how much work must be done to bring it to a stop?
(1/2)m v^2 = 625(1600) Joules
divide by 1000 for kJ
that is also the work to stop it in kJ
Well, well, well, if it isn't our speedy automobile! Let me calculate those numbers for you.
To find the kinetic energy, we can use the formula:
Kinetic energy = (1/2) x mass x velocity^2
Plugging in the numbers, we get:
Kinetic energy = (1/2) x 1.250 kg x (40 m/s)^2
Calculating that, we find the energy to be 1,000 Joules.
Now, to bring our zippy car to a stop, we need to counteract that kinetic energy with an equal amount of work. So, the amount of work needed to bring it to a stop will also be 1,000 Joules.
And since you're a curious one, I'll let you in on a little secret: That's the same amount of energy I use in an average day to make people laugh! 🤡
To calculate the kinetic energy of the automobile, we use the formula:
Kinetic Energy = (1/2) * mass * velocity^2
Step 1: Convert the mass from kg to g.
1 kg = 1000 g
So, 1.250 kg = 1250 g
Step 2: Calculate the kinetic energy.
Kinetic Energy = (1/2) * mass * velocity^2
Kinetic Energy = (1/2) * 1250 g * (40 m/s)^2
Kinetic Energy = 0.5 * 1250 g * 1600 m^2/s^2
Step 3: Convert the energy from g.m^2/s^2 to kJ.
1 J = 0.001 kJ
So, 1 g.m^2/s^2 = 0.001 kJ
Kinetic Energy = 0.5 * 1250 g * 1600 m^2/s^2
Kinetic Energy = 0.5 * 1250 g * 1600 * 0.001 kJ
Kinetic Energy = 1000 kJ
Therefore, the energy of the automobile is 1000 kJ.
To calculate the work done to bring the automobile to a stop, we need to use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
Step 4: Calculate the work done.
Work Done = Change in Kinetic Energy
Since the automobile is brought to a stop, its final kinetic energy is zero.
Work Done = Final Kinetic Energy - Initial Kinetic Energy
Work Done = 0 - 1000 kJ
Work Done = -1000 kJ
Therefore, the work done to bring the automobile to a stop is -1000 kJ. The negative sign indicates that work is done on the automobile to stop its motion.
To calculate the energy of the automobile, we need to find its kinetic energy. The kinetic energy (KE) formula is given by:
KE = 1/2 * m * v^2
where:
m = mass of the automobile
v = velocity of the automobile
Given:
m = 1.250 kg
v = 40 m/s
Let's substitute the given values into the formula:
KE = 1/2 * 1.250 kg * (40 m/s)^2
Now we can simplify the equation:
KE = 1/2 * 1.250 kg * 1600 m^2/s^2
KE = 1000 J
To convert Joules to kilojoules (kJ), divide by 1000:
KE = 1000 J / 1000 = 1 kJ
Therefore, the energy of the automobile is 1 kJ.
To calculate the work required to bring the automobile to a stop, we need to use the work-energy theorem, which states that the work done on an object is equal to its change in kinetic energy.
The work (W) formula can be written as:
W = ΔKE
Substituting the values:
W = 0 J - 1000 J (initial KE - final KE)
W = -1000 J
The negative sign indicates that work is done against the motion to bring the automobile to a stop.
Therefore, the work done to bring the automobile to a stop is -1000 J.