Car A has a mass of 1000kg and a speed of 60km/h, and car b has a mass of 2000kg and a speed of 30km/h. what is the ratio of kinetic energy of car A to that of car b?
KE1 = m1•v1²/2,
KE2 = m2•v2²/2,
KE1/ KE2 = m1•v1²/ m2•v2²,
where
m1=1000 kg, v1 = 60000/3600 m/s,
m2=2000 kg, v2 = 30000/3600 m/s
KE1= M1.v1'2/2
KE2= M2V2'2/2
KE1= [(1000kg)(277.89m'2/s'2)/2]
= 138944.45J
KE2= [(2000kg) (69.3889'2/s'2)/2]
= 69388.9J
KE1/KE2= 138944.45J/69388.9J
=2.00
To find the ratio of kinetic energy (KE) of car A to that of car B, we'll need to use the formula for kinetic energy:
KE = (1/2) * mass * velocity^2
For Car A:
Mass (m1) = 1000 kg
Velocity (v1) = 60 km/h
For Car B:
Mass (m2) = 2000 kg
Velocity (v2) = 30 km/h
First, let's convert the velocities from km/h to m/s:
Velocity A (v1) = 60 * (1000/3600) = 16.67 m/s
Velocity B (v2) = 30 * (1000/3600) = 8.33 m/s
Now we can calculate the kinetic energies:
KE1 = (1/2) * m1 * v1^2 = (1/2) * 1000 * 16.67^2
KE2 = (1/2) * m2 * v2^2 = (1/2) * 2000 * 8.33^2
Let's calculate the values:
KE1 = 1/2 * 1000 * 277.78
KE1 = 138,890 Joules
KE2 = 1/2 * 2000 * 69.44
KE2 = 69,440 Joules
Now, we can find the ratio of kinetic energy of car A (KE1) to that of car B (KE2):
Ratio = KE1 / KE2
Ratio = 138,890 / 69,440
Ratio ≈ 2
Therefore, the ratio of the kinetic energy of car A to that of car B is approximately 2:1.
To find the ratio of the kinetic energy of car A to that of car B, we need to calculate the kinetic energy for each car separately and then compare the results.
The formula for calculating kinetic energy is:
Kinetic Energy = (1/2) * mass * speed^2
For Car A, we have:
Mass (m1) = 1000 kg
Speed (v1) = 60 km/h
First, we need to convert the speed from km/h to m/s, since the formula requires the speed to be in meters per second. We know that 1 km/h is equal to 1000 m/3600 s (1 hour has 3600 seconds). So:
Speed (v1) = 60 km/h * (1000 m/3600 s) = 16.67 m/s (rounded to two decimal places)
Now we can calculate the kinetic energy of Car A:
Kinetic Energy (K1) = (1/2) * m1 * v1^2
= (1/2) * 1000 kg * (16.67 m/s)^2
≈ 139,196.81 joules (rounded to two decimal places)
For Car B, we have:
Mass (m2) = 2000 kg
Speed (v2) = 30 km/h
Again, we need to convert the speed from km/h to m/s:
Speed (v2) = 30 km/h * (1000 m/3600 s) = 8.33 m/s (rounded to two decimal places)
Now we can calculate the kinetic energy of Car B:
Kinetic Energy (K2) = (1/2) * m2 * v2^2
= (1/2) * 2000 kg * (8.33 m/s)^2
≈ 69,437.5 joules (rounded to two decimal places)
Finally, we can determine the ratio of the kinetic energy of Car A to that of Car B:
Ratio = K1 / K2
= 139,196.81 joules / 69,437.5 joules
≈ 2.00 (rounded to two decimal places)
Therefore, the ratio of the kinetic energy of Car A to that of Car B is approximately 2.00.