A lever with an effort arm of 10 meters and a load arm of 2 meters is used to lift an object weighing 220 Newtons to a height of 4 meters. If 400Joules of work is done, how much force must have been applied? (1 point)

Question

• 4000 N
• 800 N
O 100 N
O 1600 N

Answer 1

To find the force applied using a lever, we can use the principle of levers which states that:

\[ \text{Effort} \times \text{Effort Arm} = \text{Load} \times \text{Load Arm} \]

Given:

• Load (weight of the object) = 220 N
• Load Arm = 2 m
• Effort Arm = 10 m
• Work done = 400 J

First, we can calculate the effort (the force we need to apply) using the lever formula:

\[ \text{Effort} \times 10 , \text{m} = 220 , \text{N} \times 2 , \text{m} \]

Calculating the right side:

\[ 220 , \text{N} \times 2 , \text{m} = 440 , \text{N} \cdot \text{m} \]

Now we can solve for Effort:

\[ \text{Effort} \times 10 = 440 \]

\[ \text{Effort} = \frac{440}{10} = 44 , \text{N} \]

This is the force applied through the lever. However, the answer choices don't include it, and it seems the effort applied here is not reflected in the work done information.

Let's check the work done using the known values:

The work done (W) is given by the formula:

\[ W = \text{Effort} \times \text{Distance} \]

Given the work done is 400 J and knowing the distance moved by the effort (which is the distance the object rises, which is 4 m), we can find the applied force.

Substituting for \( W \):

\[ 400 = \text{Effort} \times 4 \]

Solving for Effort:

\[ \text{Effort} = \frac{400}{4} = 100 , \text{N} \]

So the correct answer is 100 N.