*I am lost on a bunch of different problems, and this is one of them. Please note that I am NOT asking for final answers, just some guidance so that I can figure out how to do the problem!!! I know that a lot of times on this site it is commented that we are fishing for answers, but I just need some guidance on some stuff I honestly cannot figure out how to do, no matter how easy it might seem to others.
A 18.0 N package of whole wheat flour is suddenly placed on the pan of a scale such as you find in grocery stores. The pan is supported from below by a vertical spring of force constant 315 N/m.
If the pan has negligible weight, find the maximum distance the spring will be compressed if no energy is dissipated by friction.
Answer expressed in cm.
Force= k*distance
Solve for distance
gsdg
19.71m
To find the maximum distance the spring will be compressed when a 18.0 N package of whole wheat flour is placed on the pan of a scale, we can use Hooke's Law.
Hooke's Law states that the force exerted by a spring is directly proportional to the distance it is stretched or compressed from its equilibrium position.
The formula for Hooke's Law is:
Force = k * distance
Where:
- Force is the force exerted by the spring (in Newtons, N)
- k is the force constant of the spring (in Newtons per meter, N/m)
- distance is the distance the spring is stretched or compressed from its equilibrium position (in meters, m)
In this problem, the force is 18.0 N and the force constant is 315 N/m. We need to solve for the maximum distance the spring will be compressed, which we'll call "d".
So the equation becomes:
18.0 N = 315 N/m * d
To solve for d, divide both sides of the equation by 315 N/m:
d = 18.0 N / 315 N/m
Simplifying the units, m (meter) on the bottom and N (Newton) on the top cancel out:
d = 0.0571 m
Finally, we convert the distance from meters to centimeters. Since 1 meter is equal to 100 centimeters, we can multiply the distance in meters by 100:
d = 0.0571 m * 100 cm/m
d = 5.71 cm
Therefore, the maximum distance the spring will be compressed is 5.71 cm.
To find the maximum distance the spring will be compressed, we need to use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.
First, let's rearrange Hooke's Law to solve for distance:
Force = k * distance
To find the distance, we need to divide both sides of the equation by the force constant:
distance = Force / k
Given that the force constant is 315 N/m and the force exerted on the spring is 18.0 N, we can substitute these values into the equation to find the maximum distance:
distance = 18.0 N / 315 N/m
To simplify this expression, we can divide the numerator and denominator by 9 N:
distance = (18.0 N / 9 N) / (315 N/m / 9 N)
By canceling out the units, we get:
distance = 2 / (35 / 9) m
To express the distance in centimeters, we need to convert meters to centimeters. Since 1 meter equals 100 centimeters, we can multiply the distance by 100:
distance = (2 / (35 / 9)) * 100 cm
Now we can simplify this expression:
distance = (2 * 9 / 35) * 100 cm
distance = (18 / 35) * 100 cm
distance ≈ 51.43 cm
Therefore, the maximum distance the spring will be compressed is approximately 51.43 cm when no energy is dissipated by friction.