During a car crash a 65kg person's head goes from traveling at 50km h-1 to stationary in 0.15s.
(a)What is the magnitude of the average net force acting on the head of a person with a 4.5kg head?
(b)How does this compare with the weight force acting on the person?
50kph = (50 /3.6) = 13.89m/sec.
Acceleration = (v/t) = 13.89/0.15, = -92.6m/sec^2.
a) Average force on head = (ma) = 4.5 x 92.6, = 416.7N.
b) Weight force = (65 x 9.8) = 637N. So force on head is (416.7/637) = 0.654 of weight force.
Well, well, well... looks like someone had a smashing time! Let's crunch some numbers and find out what's going on.
(a) To calculate the magnitude of the average net force, we can use Newton's second law: force equals mass times acceleration. In this case, the head's initial velocity is 50 km/h, which we need to convert to m/s. One kilometer has 1000 meters, and one hour has 3600 seconds, so 50 km/h is approximately 13.9 m/s.
The final velocity of the head is zero, and the time it takes to come to a stop is 0.15 seconds. Acceleration can be found using the equation acceleration equals change in velocity divided by time. So, the acceleration will be (0 - 13.9 m/s) / 0.15 s, which is approximately -92.7 m/s² (negative because the head stops).
Since we're dealing with a 4.5 kg head, we can now plug the values into Newton's second law: force equals mass times acceleration. So the average net force would be 4.5 kg × -92.7 m/s². Math time! And the result is approximately -417.15 N.
(b) Now, let's compare this force with the weight force acting on the person. The weight force can be found using the formula weight equals mass times gravity. Since we have a 65 kg person, we multiply it by the acceleration due to gravity, which is about 9.8 m/s².
So, the weight force would be 65 kg × 9.8 m/s². Another round of calculations, and the result comes out to be approximately 637 N.
Oh dear! It seems like the magnitude of the average net force is lower than the weight force acting on the person. I guess this person's head experienced a force just a fraction of the "weight" they were carrying. But hey, let's hope they're okay and can soon laugh about it! Always good to keep a sense of humor, even in physics.
To solve this problem, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. The formula is:
F = m * a
where F is the net force, m is the mass, and a is the acceleration.
Let's break down the problem step-by-step:
Step 1: Convert the speed from km/h to m/s.
Given: Initial velocity (u) = 50 km/h
We know that 1 km/h = (1/3.6) m/s
So, the initial velocity can be calculated as:
Initial velocity (u) = 50 km/h * (1/3.6) m/s = 13.89 m/s
Step 2: Calculate the acceleration.
We can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.
Given: Final velocity (v) = 0 m/s
Time taken (t) = 0.15 s
Using the equation, we can rearrange it to solve for acceleration:
0 = 13.89 m/s + a * 0.15 s
-13.89 m/s = 0.15 a
a = (-13.89 m/s) / (0.15 s)
a ≈ -92.6 m/s²
Note: The negative sign indicates that there is deceleration (opposite to the direction of motion).
Step 3: Calculate the net force.
Given: Mass (m) = 4.5 kg
Using Newton's second law of motion (F = m * a), we can calculate the net force:
F = 4.5 kg * (-92.6 m/s²)
F ≈ -416.7 N
The magnitude of the average net force is approximately 416.7 N.
Step 4: Compare with the weight force.
The weight force acting on an object is given by the formula:
Weight force = mass * acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s².
Weight force = 4.5 kg * 9.8 m/s²
Weight force ≈ 44.1 N
Comparing the magnitude of the average net force (-416.7 N) with the weight force (44.1 N), we can see that the net force is much larger due to the sudden deceleration during the car crash.
To find the magnitude of the average net force acting on the head during a car crash, we can use Newton's second law of motion, which states that force equals mass multiplied by acceleration (F = ma).
(a) To start, we need to calculate the acceleration experienced by the head during the crash. We can use the equation for acceleration, which is the change in velocity divided by the change in time (a = (vf - vi) / t).
Given:
Mass of the person's head (m) = 4.5kg
Initial velocity (vi) = 50km/h = 50,000m/3600s = 13.89m/s (Converting km/h to m/s)
Final velocity (vf) = 0m/s
Time taken (t) = 0.15s
Substituting these values into the equation for acceleration:
a = (0 - 13.89) / 0.15
Calculating the acceleration:
a = -13.89 / 0.15
a ≈ -92.6 m/s²
Since the deceleration during the crash is negative (opposite direction to the initial velocity), we take the magnitude of the acceleration.
Next, we can use Newton's second law to find the force:
F = ma
F = 4.5kg * (-92.6 m/s²)
Calculating the magnitude of the average net force acting on the head:
F ≈ -416.7 N
The magnitude of the average net force acting on the person's head during the car crash is approximately 416.7 Newtons.
(b) To compare this with the weight force acting on the person, we need to calculate the weight force. The weight force can be found using the equation F = mg, where m is the mass of the person and g is the acceleration due to gravity (approximately 9.8 m/s²).
Given:
Mass of the person (m) = 65kg
Acceleration due to gravity (g) = 9.8 m/s²
Calculating the weight force:
F = mg
F = 65kg * 9.8 m/s²
F ≈ 637 N
The weight force acting on the person is approximately 637 Newtons.
Comparing the magnitude of the average net force during the crash (416.7 N) with the weight force (637 N), we can see that the average net force is lower than the weight force.