compute the kinetic energy of an 1800 lb automobile traveling at 30 mi/hr. how many times as great is the kinetic energy if the velocity is doubled? compute the kinetic energy, in erg and in joules, of a 2 gram bullet travelling at 500 m/sec.

Mass = 1800Lb * 0.454kg/Lb = 817.2 kg

V=30mi/h * 1600m/mi * 1h/3600s=13.33 m/s

KE=0.5m*V^2 = 0.5*817.2*13.33^2 = 72,604 Joules.

KE = 0.5m*(2V^2) = .5m*4V^2 = 4 times
as great.

KE = 0.5*0.002*500^2 = 250 J.

To compute the kinetic energy of an automobile, you can use the formula:

Kinetic Energy = 0.5 * mass * velocity^2

1. First, convert the weight of the automobile from pounds to kilograms:
1800 lb = 1800 lb * (0.4536 kg / 1 lb) = 816.48 kg

2. Next, convert the velocity from miles per hour to meters per second:
30 mi/hr = 30 mi/hr * (1609.34 m / 1 mi) * (1 hr / 3600 s) = 13.41 m/s

3. Now, calculate the initial kinetic energy of the automobile:
Kinetic Energy = 0.5 * mass * velocity^2 = 0.5 * 816.48 kg * (13.41 m/s)^2 = 73,201.64 Joules

If the velocity is doubled, the new velocity would be 2 * 13.41 m/s = 26.82 m/s.

4. Calculate the new kinetic energy:
New Kinetic Energy = 0.5 * mass * velocity^2 = 0.5 * 816.48 kg * (26.82 m/s)^2 = 292,806.57 Joules

The new kinetic energy is 292,806.57 Joules, which is approximately 4 times as great as the initial kinetic energy.

Now, let's compute the kinetic energy of a 2 gram bullet traveling at 500 m/s:

1. Convert the mass of the bullet from grams to kilograms:
2 grams = 2 grams * (0.001 kg / 1 gram) = 0.002 kg

2. Calculate the kinetic energy:
Kinetic Energy = 0.5 * mass * velocity^2 = 0.5 * 0.002 kg * (500 m/s)^2 = 250 Joules

The kinetic energy of the 2 gram bullet is 250 Joules.

To convert the kinetic energy from Joules to ergs, we need to use the following conversion factor:

1 Joule = 10^7 ergs

So, to convert 250 Joules to ergs:

250 Joules = 250 * 10^7 ergs = 2.5 * 10^9 ergs

Therefore, the kinetic energy of the 2 gram bullet is 2.5 * 10^9 ergs.

To compute the kinetic energy of an object, we use the formula:

Kinetic Energy (KE) = 0.5 * mass * velocity^2

1. For the first question, let's compute the kinetic energy of an 1800 lb (pound) automobile traveling at 30 mi/hr.

Step 1: Convert pounds to kilograms
To convert pounds to kilograms, we need to divide the weight in pounds by the conversion factor 2.205. Therefore, 1800 lb = 1800 / 2.205 kg ≈ 816.33 kg.

Step 2: Convert miles per hour to meters per second
To convert miles per hour to meters per second, multiply the speed in mph by the conversion factor 0.44704. Therefore, 30 mi/hr = 30 * 0.44704 m/s ≈ 13.4112 m/s.

Step 3: Calculate the kinetic energy using the formula
KE = 0.5 * mass * velocity^2
KE = 0.5 * 816.33 kg * (13.4112 m/s)^2
KE ≈ 693,037.53 Joules

So, the kinetic energy of the automobile traveling at 30 mi/hr is approximately 693,037.53 Joules.

2. Now let's calculate how many times greater the kinetic energy would be if the velocity is doubled.

Step 1: Double the velocity
The original velocity is 13.4112 m/s. Doubling it results in 26.8224 m/s.

Step 2: Calculate the new kinetic energy using the formula
KE = 0.5 * mass * velocity^2
Since the mass remains the same, we only need to change the velocity:
KE = 0.5 * 816.33 kg * (26.8224 m/s)^2
KE ≈ 2,772,690.12 Joules

The new kinetic energy is approximately 2,772,690.12 Joules.

To determine how many times greater the new kinetic energy is compared to the original, we divide the new kinetic energy by the original kinetic energy:
2,772,690.12 Joules / 693,037.53 Joules ≈ 4

Therefore, the kinetic energy is approximately 4 times greater when the velocity is doubled.

3. For the second question, let's compute the kinetic energy of a 2-gram bullet traveling at 500 m/s.

Step 1: Convert grams to kilograms
To convert grams to kilograms, we divide the mass in grams by 1000. Therefore, 2 g = 2 / 1000 kg = 0.002 kg.

Step 2: Calculate the kinetic energy using the formula
KE = 0.5 * mass * velocity^2
KE = 0.5 * 0.002 kg * (500 m/s)^2
KE = 0.5 * 0.002 kg * 250,000 m^2/s^2
KE = 250 Joules

So, the kinetic energy of the 2-gram bullet traveling at 500 m/s is 250 Joules.

To convert the kinetic energy to ergs, we multiply by the conversion factor: 1 Joule = 10^7 ergs.
250 Joules * (10^7 ergs/Joule) = 2.5 * 10^9 ergs

Therefore, the kinetic energy of the bullet is 2.5 * 10^9 ergs or 250 Joules.