Illinois Jones is being pulled from a snake pit with a rope that breaks if the tension in it exceeds 755 N.
If Illinois Jones has a mass of 70.0 kg and the snake pit is 3.90m deep, what is the minimum time that is required to pull our intrepid explorer from the pit?
Someone please help I feel like i'm inadequate.
Well, let me put your mind at ease, inadequate friend. I can help you with that!
To begin, we need to calculate the gravitational force acting on Illinois Jones. The formula for gravitational force is F = mg, where m is his mass (70.0 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
So, the gravitational force pulling him down is F = (70.0 kg)(9.8 m/s^2) = 686 N. Now we know that the tension in the rope must exceed 755 N in order for it to hold him.
Since the minimum tension required to prevent the rope from breaking is 755 N, we need to find the force that must be exerted to pull Illinois Jones up the pit.
The net force acting on him is given by the equation F = ma, where a is the acceleration. Since he's being pulled upwards, we can assume this acceleration is positive. So we rearrange the equation to find the force:
F = ma
F = (70.0 kg)(9.8 m/s^2 + a)
Since he is being pulled upwards, the force equation becomes:
F = (70.0 kg)(9.8 m/s^2 + a) > 755 N
Solving this equation for the acceleration:
a > (755 N)/(70.0 kg) - 9.8 m/s^2
a > 0.93 m/s^2
Now, to find the minimum time required, we need to calculate the time it takes to traverse the 3.9 m deep pit using an average velocity. Let's assume his average velocity is v, then we can use the equation:
s = vt
3.9 m = v * t
Rearranging the equation, we get:
t = (3.9 m) / v
Now, we can use the equation v = u + at, where u is the initial velocity, which we assume to be 0 m/s since he starts from rest. Plugging in the values, we have:
v = u + at
v = 0 m/s + (0.93 m/s^2)(t)
Now, we can substitute this value of v back into the time equation:
t = (3.9 m) / (0 m/s + (0.93 m/s^2)(t))
Solving this equation, we find:
t ≈ 4.19 seconds
So, the minimum time required to pull Illinois Jones out of the pit is approximately 4.19 seconds. I hope this helps, and remember, you're not inadequate – you're just exploring the wonderful world of physics!
You are not inadequate! I'm here to help you step-by-step with this problem.
To find the minimum time required to pull Illinois Jones from the snake pit, we can use the concept of work and energy. The work done in pulling Jones out of the pit will be equal to the potential energy gained by him.
The potential energy (PE) of an object is given by the formula:
PE = mgh
Where:
m = mass of the object (70.0 kg in this case)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height of the pit (3.90 m in this case)
The work done (W) is equal to the change in potential energy:
W = PE
Since W = Fd (force times distance), and in this case, the force is equal to the tension in the rope, we can write:
W = Td
Where:
T = tension in the rope
d = distance pulled
To find the tension in the rope, we can use Newton's second law of motion:
T = mg
Now, we can set up an equation to solve for the minimum time (t) required to pull Jones out of the pit:
W = Td = mgh
Substituting T = mg, we get:
mgd = mgh
Canceling out "m" from both sides, we get:
gd = gh
Dividing both sides by g, we get:
d = h
Therefore, the minimum distance pulled (d) is equal to the height of the pit (h).
Now, to find the minimum time (t), we can use the formula for average speed:
Speed = Distance / Time
Rearranging the formula, we get:
Time = Distance / Speed
In this case, the speed at which Illinois Jones is being pulled will depend on the tension in the rope and the mass of Jones, as the rope will break if the tension exceeds 755 N. So, we can write:
Time = Distance / (Tension / Mass)
Substituting the values we have, we get:
Time = h / (755 N / 70.0 kg)
Now, we can calculate the minimum time required:
Time = (3.90 m) / (755 N / 70.0 kg)
Time ≈ 0.333 seconds
Therefore, the minimum time required to pull Illinois Jones from the snake pit is approximately 0.333 seconds.
To find the minimum time required to pull Illinois Jones from the pit, we need to consider the forces acting on him and use Newton's laws of motion.
First, let's consider Illinois Jones's weight. The weight can be calculated using the formula:
Weight = mass × acceleration due to gravity
Weight = 70.0 kg × 9.8 m/s² (acceleration due to gravity is approximately 9.8 m/s²)
Weight = 686 N
Now, let's analyze the forces acting on Illinois Jones while he is being pulled from the pit. Since the rope is the only object that can exert a force on him, we can equate this force to the weight:
Force on the rope = Weight
The force on the rope can also be calculated using Newton's second law of motion:
Force on the rope = mass × acceleration
Since Illinois Jones is being pulled vertically upward, the acceleration will be in the opposite direction to gravity. So, the acceleration can be given by:
Acceleration = (final velocity - initial velocity) / time
Here, final velocity is zero as Illinois Jones comes to rest when pulled out of the pit, and initial velocity is given by:
Initial velocity = √(2 × acceleration due to gravity × distance)
Plug in the given values:
Initial velocity = √(2 × 9.8 m/s² × 3.9 m)
Initial velocity ≈ 7.60 m/s
Now, rearrange the equation for acceleration to solve for time:
time = (final velocity - initial velocity) / acceleration
Since the final velocity is zero:
time = (-initial velocity) / acceleration
Substitute the values:
time = (-7.60 m/s) / (9.8 m/s²)
time ≈ -0.78 s
The negative sign indicates that the initial velocity and acceleration are in opposite directions. To get the positive value of time, we'll consider the magnitude:
time ≈ 0.78 s
Therefore, the minimum time required to pull Illinois Jones from the pit is approximately 0.78 seconds.