a) compute the kinetic energy in Joules of a 1600kg automibile traveling at 50.0 km/h. By what factor does the kinetic change if the speed is doubled?
KE = (1/2) * m * V^2
Try to solve for KE.
To compute the kinetic energy of the automobile, we can use the formula:
Kinetic Energy = 1/2 * mass * velocity^2
Given:
- Mass of the automobile = 1600 kg
- Velocity = 50.0 km/h
First, we need to convert the velocity from kilometers per hour to meters per second, as the formula requires the velocity in m/s.
1. To convert kilometers per hour (km/h) to meters per second (m/s), we need to multiply the velocity by a conversion factor of 1/3.6.
Velocity in m/s = (Velocity in km/h) * (1/3.6)
Velocity in m/s = 50.0 km/h * (1/3.6)
Velocity in m/s = 13.9 m/s (rounded to one decimal place)
Now, we can substitute the values into the formula to find the kinetic energy.
2. Kinetic Energy = 1/2 * mass * velocity^2
Kinetic Energy = 1/2 * 1600 kg * (13.9 m/s)^2
Kinetic Energy = 1/2 * 1600 kg * 192.1 m^2/s^2
Kinetic Energy = 138,880 Joules
The kinetic energy of the automobile is 138,880 Joules.
To find the factor by which the kinetic energy changes if the speed is doubled, we can compare the initial kinetic energy (E1) with the new kinetic energy at double the speed (E2).
3. Let's double the speed:
New Velocity = 2 * 13.9 m/s
New Velocity = 27.8 m/s
Now we can calculate the new kinetic energy (E2) using the formula.
4. E2 = 1/2 * mass * velocity^2
E2 = 1/2 * 1600 kg * (27.8 m/s)^2
E2 = 1/2 * 1600 kg * 771.24 m^2/s^2
E2 = 617,992 Joules
The new kinetic energy (E2) is 617,992 Joules.
5. To find the factor by which the kinetic energy changes, we divide E2 by E1 and take the ratio:
Factor = E2 / E1
Factor = 617,992 Joules / 138,880 Joules
Factor = 4.45 (rounded to two decimal places)
The kinetic energy changes by a factor of approximately 4.45 when the speed is doubled.