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. if the actual force is 300 n, what is the actual mechanical advantage?
a 3.33
b 1.23
c 4.15
d 2.78

Explanation:

Step1: Recall the formula for actual mechanical advantage (AMA)

The formula for actual mechanical advantage is \( AMA=\frac{F_{resistance}}{F_{effort}} \), where \( F_{resistance} \) is the force to overcome the resistance (weight of the piano) and \( F_{effort} \) is the actual force applied.

Step2: Identify the values of \( F_{resistance} \) and \( F_{effort} \)

Given that \( F_{resistance} = 1000\ N \) (weight of the piano) and \( F_{effort}=300\ N \) (actual force applied).

Step3: Calculate the actual mechanical advantage

Substitute the values into the formula: \( AMA = \frac{1000\ N}{300\ N}=\frac{10}{3}\approx 3.33 \)

Answer:

a. 3.33