An advertisement claims that a particular automobile can "stop on a dime". What net force would actually be necessary to stop an automobile of mass 850kg traveling initially at a speed of 38.0km/h in a distance equal to the diameter of a dime, which is 1.8cm ?
Vo = 38km/h = 38000m/3600s = 10.56 m/s.
a = (V^2-Vo^2)/2d = (0-10.56^2)/0.018m =
6195 m/s^2.
F = m*a = 850 * 6195 = 5,265,920 N.
Maybe we shouldn't stop it on a dime!
Well, stopping on a dime is quite the feat! To calculate the net force required, we'll need to determine the deceleration first. First, let's convert the initial speed from km/h to m/s.
38.0 km/h = 10.6 m/s (approximately, because numbers make me dizzy!)
Now let's calculate the deceleration using the equation:
vf^2 = vi^2 + 2ad
Where vf is the final velocity (0 m/s since we want to stop), vi is the initial velocity, a is the deceleration, and d is the distance traveled.
Plugging in the known values:
0^2 = (10.6 m/s)^2 + 2a(0.018 m)
Simplifying:
a = (-10.6 m/s)^2 / (2 * 0.018 m)
Calculating:
a ≈ -315.111 ms^2
Now, we know that force (F) is equal to the mass (m) multiplied by the acceleration (a):
F = m * a
Plugging in the values:
F = 850 kg * -315.111 ms^2
Calculating:
F ≈ -267,844.35 N
So, the net force necessary to stop the automobile on a dime would be approximately -267,844.35 Newtons (or about -26,000 times the weight of that dime). That's one powerful stopping force! Just be careful not to get your fingers stuck in the change slot!
To determine the net force necessary to stop the automobile, we can use the principle of work and energy.
1. First, let's convert the initial speed of the automobile from km/h to m/s:
38.0 km/h = 38.0 * (1000 m / 3600 s) = 10.6 m/s
2. Next, we can calculate the initial kinetic energy (KE) of the automobile using the formula:
KE = 0.5 * mass * velocity^2
Plugging in the given values:
KE = 0.5 * 850 kg * (10.6 m/s)^2
= 0.5 * 850 kg * 112.36 m^2/s^2
≈ 47,815 J
3. In order to stop the automobile within a distance equal to the diameter of a dime (1.8 cm), we need to bring the kinetic energy to zero. This requires applying a force in the opposite direction of motion to slow down and eventually stop the automobile.
4. The work (W) done by the net force (F) can be calculated using the formula:
W = F * d
Where:
W is the work done (in joules),
F is the net force (in newtons), and
d is the distance over which the force is applied (in meters).
Plugging in the given values:
0 = F * 0.018 m
Since the work done is zero (kinetic energy to bring to zero), the net force required must also be zero. This means that no net force is necessary to stop the automobile within the distance equal to the diameter of a dime.
Therefore, the claim made by the advertisement that the automobile can "stop on a dime" is inaccurate.
To determine the net force required to stop the automobile, we can use the principles of physics, specifically the equations of motion and the concept of work and energy.
First, we need to convert the given quantities into SI units:
- Mass of the automobile, m = 850 kg
- Initial velocity of the automobile, u = 38.0 km/h = 10.56 m/s (since 1 km/h = 0.2778 m/s)
- Distance for stopping, s = diameter of a dime = 1.8 cm = 0.018 m
Next, we can calculate the deceleration (negative acceleration) required to bring the automobile to a stop using the equation:
v^2 = u^2 + 2as
Where:
- v is the final velocity (which is 0, since the automobile comes to a stop)
- u is the initial velocity
- a is the acceleration or deceleration
- s is the distance traveled
Rearranging the equation to solve for the deceleration, we have:
a = (v^2 - u^2) / (2s)
Plugging in the given values:
a = (0 - (10.56)^2) / (2 * 0.018)
Simplifying:
a = -1110.24 / 0.036
a = -30840 m/s^2
Now, we know the deceleration (negative acceleration) required to stop the automobile is -30840 m/s^2.
Finally, we can calculate the net force (F) required using Newton's second law of motion:
F = ma
Where:
- F is the net force
- m is the mass
- a is the acceleration or deceleration
Substituting the given values:
F = 850 kg * (-30840 m/s^2)
F ≈ -26,244,000 N (Note: The negative sign indicates that the force is in the opposite direction of the motion.)
Therefore, the net force necessary to stop the automobile of mass 850 kg traveling initially at a speed of 38.0 km/h in a distance equal to the diameter of a dime is approximately 26,244,000 Newtons in the opposite direction of the motion.