An aricraft carrier has a mass of 8.6*10^7 kg and can cruise at 80 km/h.
a) What is the work required to stop it?
B) If only half of the work required to stop it is done, what is its final speed in km/h
For a) I found 2.123*10^10 which is the right answer but I cant find b i don't understand
80 km/h = 80000/3600 =22.22 m/s
W=ΔKE= mv²/2=8.6•10⁷•(22.22) ²/2=2.123•10¹º J
W₁=W/2 =1.062•10¹⁰J
W₁=ΔKE₁=mv₁²/2
v₁=sqrt(2W₁/m) = 15.71 m/s
To solve part b), you need to apply the principle of conservation of energy. The work required to stop the aircraft carrier in part a) can be considered as the total initial kinetic energy of the carrier.
The kinetic energy of an object can be calculated using the formula:
KE = 0.5 * mass * velocity^2
Given that the mass of the aircraft carrier is 8.6*10^7 kg and its initial speed is 80 km/h, we can calculate its initial kinetic energy:
KE_initial = 0.5 * (8.6*10^7) * (80^2)
Now, if only half of the work required to stop the carrier is done, it means that half of its initial kinetic energy is lost. Therefore, the final kinetic energy of the carrier will be half of the initial kinetic energy:
KE_final = 0.5 * KE_initial
To find the final speed, we rearrange the kinetic energy formula:
KE_final = 0.5 * mass * velocity_final^2
Dividing both sides of the equation by 0.5 * mass:
velocity_final^2 = (2 * KE_final) / mass
Substituting the values, we can find the final speed of the carrier in km/h:
velocity_final^2 = (2 * (0.5 * (8.6*10^7) * (80^2))) / (8.6*10^7)
velocity_final^2 = (0.5 * (8.6*10^7) * (80^2)) / (8.6*10^7)
velocity_final^2 = (0.5 * (80^2))
velocity_final^2 = 3200
velocity_final = √3200
velocity_final ≈ 56.57 km/h
Therefore, the final speed of the aircraft carrier, if only half of the work required to stop it is done, is approximately 56.57 km/h.
To solve part a) first, we need to calculate the work required to stop an aircraft carrier.
The work done on an object can be calculated using the formula:
Work = Force × Distance × Cosθ
In this case, we need to bring the aircraft carrier to a complete stop, so the distance is the distance traveled at a constant speed. We can calculate the distance using the formula:
Distance = Speed × Time
Given that the aircraft carrier can cruise at 80 km/h, we need to determine the time it takes to stop the carrier. To do this, we need additional information such as the deceleration or the force applied to stop the carrier. Unfortunately, this information is not provided in the given question. Therefore, we cannot calculate the work required to stop the aircraft carrier accurately.
However, we can provide a general approach to solving part b) by assuming a constant deceleration.
To find the final speed after performing only half of the work required to stop the carrier, we need to use the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.
The initial kinetic energy (KE) can be calculated using the formula:
KE = (1/2) × Mass × (Initial Speed)^2
Since we want to perform only half of the work, the final kinetic energy will be equal to half of the initial kinetic energy:
Final KE = (1/2) × (1/2) × Mass × (Initial Speed)^2
Now, we can find the final speed by solving for it in the kinetic energy equation:
Final Speed = √(2 × Final KE / Mass)
Substituting the values given in the question:
Final Speed = √(2 × (1/2) × (8.6 × 10^7 kg) × (80 km/h)^2 / (8.6 × 10^7 kg))
After performing the calculations, you should be able to determine the final speed of the aircraft carrier when only half of the work required to stop it is done.