a 1200-kg automobile travels at a speed of 90-km/h (a)what is the kinetic energy? (b) what is the net work that would be required to bring it to a stop?
(a) Convert 90 km/h to m/s, and calculate (1/2) M V^2. (The answer to b) is the same as (a).
The stopping distance of a vehicle is an important safety factor. Assuming a constant braking force, use the work-energy theorem to show that a vehicle's stopping distance is proportional to the square of its initial speed. If an automobile traveling at 45 km/h is brought to a stop in 50 m, what would be the stopping distance for an initial speed of 90 km/h?
To calculate the kinetic energy of the automobile, we can use the formula:
Kinetic energy = 0.5 * mass * velocity^2
(a) To find the kinetic energy:
Given:
Mass of the automobile (m) = 1200 kg
Speed of the automobile (v) = 90 km/h
First, we need to convert the speed from km/h to m/s since the formula requires the velocity to be in meters per second.
1 km = 1000 m
1 hour = 3600 seconds
Converting 90 km/h to m/s:
90 km/h * (1000 m/1 km) * (1/3600 h/1 s) = 25 m/s
Now, we can substitute the values into the formula:
Kinetic energy = 0.5 * 1200 kg * (25 m/s)^2
Kinetic energy = 0.5 * 1200 kg * 625 m^2/s^2
Kinetic energy = 375,000 J
Therefore, the kinetic energy of the automobile is 375,000 Joules.
(b) To find the net work required to bring the automobile to a stop, we can use the work-energy principle which states that the net work done on an object is equal to the change in its kinetic energy.
Since we want to bring the automobile to a stop, its final kinetic energy will be zero.
Net work = Change in kinetic energy
The initial kinetic energy is already calculated as 375,000 J.
The final kinetic energy is zero since the automobile is brought to a stop.
Therefore, the net work required to bring the automobile to a stop is:
Net work = 0 J - 375,000 J
Net work = -375,000 J
So, the net work required to bring the automobile to a stop is -375,000 Joules. The negative sign indicates that work is done against the motion of the automobile.
To find the kinetic energy of the automobile, we can use the formula:
Kinetic energy = (1/2) * mass * velocity^2
(a) To calculate the kinetic energy:
Step 1: Convert the mass from kilograms to grams.
Mass = 1200 kg = 1200000 g
Step 2: Convert the velocity from km/h to m/s.
Velocity = 90 km/h = 25 m/s (1 km/h = 1000 m/3600 s)
Step 3: Plug the values into the formula and calculate:
Kinetic energy = (1/2) * 1200000 g * (25 m/s)^2
Now, let's calculate the kinetic energy.
Kinetic energy = (1/2) * 1200000 g * (25 m/s)^2
= (1/2) * 1200000 * 625 * g
= 375000000 g
Therefore, the kinetic energy of the automobile is 375,000,000 g (gram).
(b) To find the net work required to bring the automobile to a stop, we need to consider the change in kinetic energy.
The net work done is equal to the change in kinetic energy, which can be calculated as:
Net work = initial kinetic energy - final kinetic energy
Since the final kinetic energy is zero (as the automobile comes to a stop), we can calculate the net work as the negative of the initial kinetic energy.
Net work = -375,000,000 g
Therefore, the net work required to bring the automobile to a stop is -375,000,000 g (gram). Note that the negative sign indicates that work is done against the motion of the automobile.