A 7.77 kg pumpkin falls from a height of 12.3m. It hits the ground and comes to an abrupt stop in about 444 ms. What is the average force imparted by the ground (aka 'Normal Force') on the pumpkin?
1/2 m v^2 = m g h
v = √(2 g h)
f = m a
mass is 7.77 kg
acceleration is ... √(2 g h) / .444 s
Well, let's calculate it, but if the pumpkin can survive being dropped from 12.3m, I'd say it's a pretty smashing gourd! Alright, enough pumpkin puns. To find the average force, we need to use Newton's second law, which states that force equals mass multiplied by acceleration. Since the pumpkin comes to an abrupt stop, we can assume its final velocity is zero. So, let's calculate the acceleration first. We'll use the equation final velocity equals initial velocity plus acceleration times time. In this case, the initial velocity is zero, and the time is 0.444 seconds. So, solving for acceleration, we get a = (0 - 0) / 0.444 = 0 m/s². Since the acceleration is zero, the average force imparted by the ground, or the normal force, is also zero. Looks like the pumpkin didn't experience any force at all! Just a gentle landing.
To calculate the average force imparted by the ground (normal force) on the pumpkin, we need to use the equation that relates force, mass, and acceleration.
1. First, we need to find the acceleration of the pumpkin when it hits the ground. We can use the formula for acceleration due to gravity:
acceleration = g = 9.8 m/s² (assuming the pumpkin is on Earth)
2. Next, we calculate the time taken by the pumpkin to come to a stop. In this case, it is given as 444 ms, which can be converted to seconds:
time = 444 ms = 444 × 10^(-3) s = 0.444 s
3. Now, we can calculate the final velocity of the pumpkin when it hits the ground using the equation:
v = u + at
where:
v = final velocity (which is zero since the pumpkin comes to a stop)
u = initial velocity (which is the velocity when it started falling, also zero in this case)
a = acceleration
t = time
Substituting the values, we have:
0 = 0 + (9.8 m/s²) × (0.444 s)
0 = 4.3552 s (rounded to four decimal places)
4. We now know the change in velocity of the pumpkin. Using the equation:
change in velocity = final velocity - initial velocity
We can find the initial velocity:
initial velocity = final velocity - change in velocity
= 0 - 4.3552
= -4.3552 m/s (negative sign indicates direction)
5. Now, we can calculate the force using Newton's second law of motion:
force = mass × acceleration
The mass of the pumpkin is given as 7.77 kg, and the acceleration is -9.8 m/s² (negative sign indicates opposite direction).
force = (7.77 kg) × (-9.8 m/s²)
= -76.146 N (rounded to three decimal places)
Therefore, the average force imparted by the ground (normal force) on the pumpkin is approximately -76.146 Newtons (N). The negative sign indicates that the force is directed opposite to the gravitational field.