Question

diana raises a 1000 n piano a distance of 5.00 m using a set of pulleys. she pulls in 20.0 m of rope. how much effort force did diana apply if this was an ideal machine?
a 150 n
b 450 n
c 325 n
d 250 n

Explanation:

Step1: Recall Work Formula for Machines

In an ideal machine, work input equals work output. Work \( W = F \times d \), where \( F \) is force and \( d \) is distance. Let \( F_{effort} \) be the effort force, \( d_{effort} = 20.0 \, \text{m} \), \( F_{load} = 1000 \, \text{N} \), \( d_{load} = 5.00 \, \text{m} \). So \( W_{input} = W_{output} \Rightarrow F_{effort} \times d_{effort} = F_{load} \times d_{load} \).

Step2: Solve for Effort Force

Rearrange the formula: \( F_{effort} = \frac{F_{load} \times d_{load}}{d_{effort}} \). Substitute values: \( F_{effort} = \frac{1000 \, \text{N} \times 5.00 \, \text{m}}{20.0 \, \text{m}} \). Calculate numerator: \( 1000 \times 5 = 5000 \). Divide by 20: \( \frac{5000}{20} = 250 \, \text{N} \).

Answer:

d. 250 N