Questions: Sharing The two objects in the figure are balanced on the pivot. (Figure 1) Part A What is distance d? Express your answer in meters. d= m

Transcript text: Sharing The two objects in the figure are balanced on the pivot.( Figure 1) Part A What is distance $d$ ? Express your answer in meters. $d=$ $\square$ m Submit Request Answer Provide Feedback

Solution

Solution Steps

Step 1: Identify the problem

We need to find the distance $ d $ at which the two objects are balanced on the pivot.

Step 2: Understand the concept of torque

Torque ($ \tau $) is the product of the force and the distance from the pivot point. For the system to be balanced, the clockwise torque must equal the counterclockwise torque.

Step 3: Calculate the torques

The torque due to the 4.0 kg mass is $ \tau_1 = 4.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times d $.
The torque due to the 1.0 kg mass is $ \tau_2 = 1.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times (2.0 \, \text{m} + 1.0 \, \text{m}) $.

Step 4: Set up the equation for balance

For the system to be balanced: \[ \tau_1 = \tau_2 \] \[ 4.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times d = 1.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 3.0 \, \text{m} \]

Step 5: Solve for $ d $

\[ 4.0 \times d = 1.0 \times 3.0 \] \[ 4.0d = 3.0 \] \[ d = \frac{3.0}{4.0} \] \[ d = 0.75 \, \text{m} \]