I got no response so I guess I'll try again
The force needed to overcome friction and drag a person across the floor depends on the person's weight. Manuel Dexterity can drag Gil O' Teen across the floor by pulling with a force of 51 pounds. Gil's brother, Nick who weighs twice as much can be dragged across the floor by pulling with a force of 102 pounds.
A.) How does force cary with the person's weight?
How do I come up with the equation? I don't know how to do this... it's something link
Y=kX or something of the sort...
This stupid math class expects us to use pounds for force instead of newtons
weight is mg, so if you needed mass you would divide by g (32 slugs/lb)
But here there is no asking for it.
You are asked how the pulling force varies with the persons weight (mg). Hmmm. You double weight (gil, then gil's brother), and the force is doubled.
That is the question.
force=constant*weight looks to me.
To understand how force varies with a person's weight in this scenario, let's use the relationship between force, weight, and Newton's second law of motion.
Newton's second law of motion states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m * a). In this case, we can assume that the mass of each person is directly proportional to their weight.
Let's denote the weight of Manuel Dexterity as W1, the weight of Gil O' Teen as W2 (twice the weight of W1), and the force required to drag them across the floor as F1 and F2, respectively.
From the given information, we know that F1 = 51 pounds and F2 = 102 pounds. We can also assume that the acceleration remains the same for both individuals.
Since the acceleration is the same, we can compare the two situations:
For Manuel: F1 = m1 * a
For Gil: F2 = m2 * a
Since a is the same in both cases, we can divide the two equations:
F2 / F1 = (m2 * a) / (m1 * a)
Dividing both sides by a, we get:
F2 / F1 = m2 / m1
Substituting the weights:
F2 / F1 = W2 / W1
Since W2 = 2 * W1, we can rewrite the equation as:
F2 / F1 = 2 * W1 / W1
Simplifying further:
F2 / F1 = 2
Therefore, the force required to overcome friction and drag a person across the floor (in this scenario) is directly proportional to their weight. In other words, if the weight of a person doubles, the force required to drag them across the floor also doubles.
To summarize, the equation that describes the relationship between force and weight in this scenario is:
F = 2W, where F is the force required to drag the person and W is their weight.
To determine the relationship between force and weight, 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.
In this case, the acceleration can be thought of as how easily the person can be dragged across the floor, which is influenced by the presence of friction and drag forces. Since we are assuming the acceleration remains constant, we can simplify the equation to F = m × a, where F represents force, m represents mass, and a represents acceleration.
Now, we know that weight is a force, specifically the force exerted by gravity on an object. And since 1 pound is equal to 0.454 kilograms, we can convert the weight from pounds to mass in kilograms. The formula to convert from weight to mass is m = W / g, where W is the weight and g is the acceleration due to gravity (which is approximately 9.8 m/s^2).
Using this information, we can write the equation as F = (W / g) × a.
Let's apply this equation to determine the relationship between force and weight for Manuel Dexterity and Gil O' Teen.
For Manuel Dexterity, the force (F) is 51 pounds, and Gil O' Teen's weight (W) is 1 times g (let's call it W1).
For Gil's brother, Nick, the force (F) is 102 pounds, and Nick's weight (W) is 2 times g (let's call it W2).
Now we can set up the equations:
For Manuel Dexterity:
51 = (W1 / g) × a (Equation 1)
For Gil's brother, Nick:
102 = (W2 / g) × a (Equation 2)
By dividing Equation 2 by Equation 1, we can eliminate the acceleration:
102 / 51 = (W2 / g) / (W1 / g)
Simplifying the equation, we get:
2 = W2 / W1
From this, we can conclude that the force required to drag a person across the floor is directly proportional to their weight. In other words, if the weight of an object doubles, the force required to drag it also doubles.