I need step by step explanation of the following problem. Using the lever system equation F1x=F2(d-x)solve the following problem: A screwdriver 9 in. long is used as a lever to open a can of paint. The tip of the screwdriver is placed under the lip of the can with the fulcrum 0.15 in. from the lip. A force of 30 lb. is applied to the other end of the screwdriver. Find the force on the lip of the can. Very confusing to me please explain. Thanks!!!!!!!!!!
The force on the handle is multiplied by the ratio of the distance from the fulcrum.
The product of force*distance for each side is the same.
So, plug in the numbers and you will see that since the handle is 60 times as long as the tip, the force applied to the tip is 30 times as great.
F1 * .15 = 30 * 9
F1 = 30*9/.15 = 540
This answer is completely wrong! F1=1770lbs., according to the answer section in the book Aufmann and Lockwood.
Sure! Let's break down the problem step by step.
Step 1: Understanding the problem
We are given a lever system equation "F1x = F2(d - x)" and are asked to find the force on the lip of the can. The problem provides the following information:
- The screwdriver is 9 inches long.
- The fulcrum (or pivot point) is located 0.15 inches from the lip of the can.
- A force of 30 pounds is applied to the other end of the screwdriver.
Step 2: Identifying variables
Let's assign variables to the given information:
- F1 represents the force on the lip of the can (what we need to find).
- F2 represents the force applied at the other end of the screwdriver (given as 30 lb).
- x represents the distance from the fulcrum to the lip of the can (unknown).
- d represents the total length of the screwdriver (given as 9 inches).
Step 3: Understanding the lever system equation
The lever system equation, F1x = F2(d - x), is based on the principle that the net torque (or turning force) on a lever is equal to zero when the system is in equilibrium. In this equation, F1 represents the force on one side of the lever, x represents the distance from the fulcrum to that force, F2 represents the force on the other side of the lever, and (d - x) represents the distance from the fulcrum to that force.
Step 4: Applying the equation to the problem
In our case, we want to solve for F1, the force on the lip of the can. We have the values for F2 (30 lb) and d (9 inches), but we need to find the value for x.
Given that the fulcrum is 0.15 inches from the lip of the can, we can substitute the given values into the lever system equation: F1(0.15) = 30(9 - 0.15).
Step 5: Solving the equation
To solve for F1, we need to isolate it on one side of the equation. Let's begin by simplifying the equation by multiplying 30 by (9 - 0.15):
0.15F1 = 270 - 4.5
0.15F1 = 265.5
Next, divide both sides of the equation by 0.15 to solve for F1:
F1 = 265.5 / 0.15
F1 ≈ 1770 lb (rounded to the nearest pound)
Step 6: Final answer
The force on the lip of the can is approximately 1770 pounds.
I hope this step-by-step explanation helps clarify the problem for you. Let me know if you have any further questions!
Sure! Let's break down the problem step by step and use the lever system equation to solve it.
Step 1: Understand the problem
In this problem, we have a lever system with a screwdriver being used to open a can of paint. The length of the screwdriver is 9 inches, and the fulcrum (point of rotation) is located 0.15 inches from the lip of the can. A force of 30 lb is applied to the other end of the screwdriver. We need to find the force applied to the lip of the can.
Step 2: Identify the variables
Let's assign variables to the given quantities:
- F1: Force applied to the lip of the can (the unknown we want to find)
- F2: Force applied to the other end of the screwdriver (30 lb)
- d: Distance from the fulcrum to the point where the force F1 is applied (unknown)
- x: Distance from the fulcrum to the lip of the can (0.15 inches)
Step 3: Use the lever system equation
The lever system equation states that the product of the force and its distance from the fulcrum on one side of the lever is equal to the product of the force and its distance from the fulcrum on the other side of the lever. Mathematically, it can be written as F1x = F2(d-x).
Step 4: Substitute the known values into the equation
Let's substitute the known values into the equation:
F1(0.15) = 30(d-0.15).
Step 5: Simplify the equation
Now, we can simplify and solve the equation to find F1. Distribute F1 and 30 into the parentheses:
0.15F1 = 30d - 4.5.
Step 6: Rearrange the equation
Since we want to solve for F1, let's rearrange the equation:
0.15F1 = 30d - 4.5.
Divide both sides of the equation by 0.15 to isolate F1:
F1 = (30d - 4.5) / 0.15.
Step 7: Solve for F1
Now, you can simplify and calculate F1. Let's divide 4.5 by 0.15 and get:
F1 = (30d - 4.5) / 0.15
F1 = (30d - 4.5) / 0.15
F1 = 200d - 30.
So, the force applied to the lip of the can is given by F1 = 200d - 30, where d is the distance from the fulcrum to the point where the force F1 is applied.
To find the specific force applied to the lip of the can, you will need to calculate the value of d based on the given information or any additional information provided in the problem. Once you have obtained the value of d, substitute it into the equation F1 = 200d - 30 to find the force applied to the lip of the can.