Illinois Jones is being pulled from a snake pit with a rope that breaks if the tension in it exceeds 755 .
If Illinois Jones has a mass of 70.0 and the snake pit is 3.90 deep, what is the minimum time that is required to pull our intrepid explorer from the pit?
Can anyone help?
Confused
It is a very nice problem, except that the question lacks units. I will assume metric units, which will make g = 9.8 m/s/s.
I restate the problem as follows:
"Illinois Jones is being pulled from a snake pit with a rope that breaks if the tension in it exceeds F = 755 N.
If Illinois Jones has a mass m of 70.0 kg and the snake pit is h=3.90 m deep, what is the minimum time that is required to pull our intrepid explorer from the pit? "
The force on the rope just to suspend Jones in the air would be mg=686N.
Reserve capacity for acceleration (assume the rope has no mass) is therefore 755-686=69N
Mass, m = 70 kg
Using F=ma
Acceleration, a = 69/70 kg = 0.986 m/s/s
Assuming the lift starts from initial velocity v0=0 m/s,
the time t (seconds) required to lift him through h=3.9 m is given by
h = v0.t + (1/2)at²
in which all variables are known except t.
So substitute all the known values and solve the resulting equation for t (in seconds). Do not retain the negative value of t. I believe it is under 3 seconds.
man 14 years later i have this same problem....
Me too. I am ready to be through with physics.
Well, I'm here to help, whether you're confused or not! Let's try to unravel this snake pit puzzle.
To find the minimum time required to pull out Illinois Jones, we need to consider a few things. First, let's calculate the force needed to lift him out of the pit.
The force required is equal to Jones' weight, which we can calculate using his mass and the acceleration due to gravity (which is approximately 9.8 m/s²). So, the force required is:
Force = mass x acceleration due to gravity
Force = 70.0 kg x 9.8 m/s²
Force = 686.0 N
Now, we'll use this force to determine the tension in the rope. To do this, we divide the force by the depth of the pit:
Tension = Force / depth of the pit
Tension = 686.0 N / 3.90 m
Tension ≈ 176.15 N
Uh-oh! The tension in the rope is less than 755 N, so it won't break. Phew!
As for the minimum time required, it depends on various other factors, such as the pulling force applied and the friction involved. Without that information, it's not possible to determine the exact time. So, let's just say it'll take "as long as it takes" to rescue Illinois Jones. I hope he's patient!
Did that help clarify things a bit?
Of course, I can help you with that!
To find the minimum time required to pull Illinois Jones from the snake pit, we need to consider the gravitational force acting on him and the tension in the rope.
Let's break it down step by step:
1. First, we need to calculate the gravitational force acting on Illinois Jones using the formula:
F_gravity = mass * acceleration due to gravity
Given that his mass is 70.0 kg and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the gravitational force:
F_gravity = 70.0 kg * 9.8 m/s²
2. Next, we need to determine the tension in the rope when Illinois Jones is being pulled from the pit. As the rope is about to break if the tension exceeds 755 N, we can say that the tension in the rope equals the gravitational force acting on him:
Tension = F_gravity
3. Now, we can determine the minimum time required to pull Illinois Jones from the pit using the equation of motion:
distance = initial velocity * time + (1/2) * acceleration * time²
In this case, the initial velocity is 0 m/s (as Illinois Jones starts from rest), the acceleration is due to gravity and is approximately 9.8 m/s², and the distance he needs to be pulled is 3.90 m (the depth of the pit).
Rearranging the equation, we get:
time = sqrt(2 * distance / acceleration)
Plugging in the given values, we have:
time = sqrt(2 * 3.90 m / 9.8 m/s²)
Calculate this to find the minimum time required.
Remember to always double-check your calculations and units!
That's it! By following these steps, you'll be able to determine the minimum time required to pull Illinois Jones from the snake pit.