hey im not good with story problems the question is david purley, survived decceration from 173km/h to 0 km/h over a distance of .660 m when his car crashed. Assume that Purley's mass is 70.0kg. What is the mgnitude of the average force acting on him during the crash? Compare the force to Purley's weight.
You need to calculate the average force. For this, we use Newton's second law, which states that:
F = m*a (where F stand for force, m is mass and a is acceleration).
Since the mass of the person was already given, we only need to calculate the persons acceleration.
One of the equations used in kinematics (science of motion) is the following:
v^2 = vo^2 - 2*a*x
(where v is the final speed in meters/s, vo the initial speed in meters/s, a the acceleration, and x the distance travelled in meters)
So, if we rewrite this formula, we find that: a= (vo^2 - v^2)/(2*x)
173 km/h = 48 m/s
so: a = (48^2 m²/s²- 0)/(2*0.660 m) = 1745.45 m/s²
Now, since Purley's mass is 70.0 kg, we find that:
F = m*a = 70.0 kg * 1745.45 m/s² = 122181,82 N = 122.18 kN
So the average force exerted on Purley's body equals 122.18 kN.
With the same formula, we can find Purley's weight (when we replace a with the gravitational acceleration g).
F = m*g = 70.0 kg * 10 m/s² = 700 N
So Purley's weight is only 700N. This means that the force acting on him during the crash is about 175 times that of his own weight.
This explains why people often experience serious bone fractures or internal injuries during a car crash. The average force acting on them is certainly large enough to break some bones.
Well, well, well, looks like David Purley was in quite a pickle there! Surviving deceleration from 173 km/h to 0 km/h is no joke. But don't worry, I'm here to help you out, with a touch of laughter!
To find the magnitude of the average force acting on Purley during the crash, we can use Newton's second law: Force = mass x acceleration. And since deceleration is just acceleration in the opposite direction, we can also say that average force = mass x deceleration.
So, we know Purley's mass is 70.0 kg, and we need to find the deceleration. To do that, we can use the equation: final velocity squared = initial velocity squared + 2 x acceleration x distance.
But wait! We need to convert the velocities from km/h to m/s because we want to use the SI units in our calculations. So, 173 km/h becomes about 47.3 m/s.
Plugging in the values:
0^2 = 47.3^2 + 2 x acceleration x 0.660
Solving this equation (a little math magic), we find that the deceleration is approximately -1007.2 m/s^2 (negative because it's deceleration).
Finally, we can calculate the average force:
Average force = mass x deceleration = 70.0 kg x (-1007.2 m/s^2)
And drumroll, please... the magnitude of the average force acting on Purley during the crash is around 70,500 N (rounded to the nearest hundred).
Now, let's compare that force to Purley's weight, shall we? His weight, my friend, is just his mass multiplied by the acceleration due to gravity, which is approximately 9.8 m/s^2. So, 70 kg x 9.8 m/s^2 gives us a weight of about 686 N.
Wow, that's quite a difference! The force acting on Purley during the crash is roughly 100 times greater than his weight. Talk about feeling the impact!
Remember, though, this is all just for educational purposes, and in reality, crashes are no laughing matter. Stay safe out there, and avoid those clown car crashes!
To find the magnitude of the average force acting on David Purley during the crash, we can use the equation:
Force = (Mass ∗ Change in Velocity) / Time
Given:
Mass (m) = 70.0 kg
Change in Velocity (Δv) = 0 km/h - 173 km/h = -173 km/h = -47.78 m/s (negative because it is a deceleration)
Distance (d) = 0.660 m
First, we need to find the time (t) it takes for the deceleration:
t = d / (Change in Velocity)
t = 0.660 m / (-47.78 m/s)
t ≈ -0.0138 s (negative because it is a deceleration)
Then, we can calculate the force:
Force = (Mass ∗ Change in Velocity) / Time
Force = (70.0 kg ∗ -47.78 m/s) / -0.0138 s
Force ≈ 24159.42 N
Therefore, the magnitude of the average force acting on David Purley during the crash is approximately 24159.42 N.
To compare this force to Purley's weight, we can find his weight using the formula:
Weight = Mass ∗ Acceleration due to Gravity
Given:
Mass (m) = 70.0 kg
Acceleration due to Gravity (g) = 9.8 m/s²
Weight = 70.0 kg ∗ 9.8 m/s²
Weight = 686 N
The force during the crash (24159.42 N) is much higher than Purley's weight (686 N), indicating the significantly higher forces experienced during the crash.
To solve this problem, we can use the equation for average force:
Average Force = (Final Velocity - Initial Velocity) / Time
However, we are not given the time. But we can calculate it using the given information. The distance, initial velocity, and final velocity are given. We can use the following equation to find the time:
Final Velocity^2 = Initial Velocity^2 + 2 × Average Acceleration × Distance
Here, the average acceleration can be calculated using the formula:
Average Acceleration = (Final Velocity - Initial Velocity) / Time
Let's calculate the time first:
1. Convert the given velocities from km/h to m/s.
- Initial Velocity = 173 km/h = (173 km/h) × (1000 m/km) × (1 h/3600 s) = 47.5 m/s
- Final Velocity = 0 km/h = (0 km/h) × (1000 m/km) × (1 h/3600 s) = 0 m/s
2. Square the final velocity:
- Final Velocity^2 = (0 m/s)^2 = 0 m^2/s^2
3. Calculate the average acceleration:
- Average Acceleration = (Final Velocity - Initial Velocity) / Time
4. Insert the values into the equation and solve for time:
- 0 m^2/s^2 = (47.5 m/s)^2 + 2 × Average Acceleration × 0.660 m
Now we can solve for Average Acceleration:
Average Acceleration = (Final Velocity - Initial Velocity) / Time
Substituting the calculated values:
0 m^2/s^2 = (47.5 m/s)^2 + 2 × Average Acceleration × 0.660 m
Simplifying and rearranging:
Average Acceleration = - [(47.5 m/s)^2] / (2 × 0.660 m)
Solve for Average Acceleration:
Average Acceleration ≈ -992.28 m/s^2
Now that we have the average acceleration, we can calculate the time:
Average Acceleration = (Final Velocity - Initial Velocity) / Time
Substituting the calculated values:
-992.28 m/s^2 = (0 m/s - 47.5 m/s) / Time
Rearranging the equation:
Time = (0 m/s - 47.5 m/s) / -992.28 m/s^2
Solve for Time:
Time ≈ 0.048 second
Now we can calculate the average force:
Average Force = (Final Velocity - Initial Velocity) / Time
Substituting the known values:
Average Force = (0 m/s - 47.5 m/s) / 0.048 second
Solve for Average Force:
Average Force ≈ -989.58 N
Since the force is negative, it means it opposes the motion. We can compare the magnitude of the average force to Purley's weight to gain a perspective:
Weight = mass × gravity
weight = 70.0 kg × 9.8 m/s^2 ≈ 686 N
Comparing the force and weight:
|Average Force| ≈ 989.58 N
Weight ≈ 686 N
The magnitude of the average force acting on David Purley during the crash is approximately 989.58 Newtons, which is greater than his weight (686 Newtons).