Two masses are suspended by cord that passes over a pulley with negligible mass. The cord also has negligible mass. One of the masses, m1, has a mass of 7.0 kg and the other mass, m2, has a mass of 3.0 kg. The pulley turns on a shaft through the center of the pulley and supports the pulley and all the masses. The vertical force of the shaft on the pulley that supports the whole system is

To determine the vertical force exerted by the shaft on the pulley that supports the system, we need to analyze the forces acting on the entire system.

### Step 1: System Overview
We have two masses, \( m_1 = 7.0 \, \text{kg} \) and \( m_2 = 3.0 \, \text{kg} \), connected by a cord passing over a pulley. The pulley and the cord are assumed to have negligible mass. The pulley is mounted on a shaft, and the shaft exerts an upward force to support the system.

Since both masses are connected by a single rope, the force on the pulley will depend on the gravitational forces acting on the two masses.

### Step 2: Forces on Each Mass
Each mass experiences a downward force due to gravity:
- Force on \( m_1 \) due to gravity: 
  \[
  F_{g1} = m_1 g = 7.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 68.6 \, \text{N}
  \]
  
- Force on \( m_2 \) due to gravity: 
  \[
  F_{g2} = m_2 g = 3.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 29.4 \, \text{N}
  \]

### Step 3: Net Force on the Pulley
The net vertical force that the shaft exerts to support the system must balance the total weight of both masses. Since the pulley is assumed to have negligible mass, the only forces we need to consider are the gravitational forces acting on \( m_1 \) and \( m_2 \).

The total gravitational force acting on the system is the sum of the forces on both masses:
\[
F_{\text{total}} = F_{g1} + F_{g2} = 68.6 \, \text{N} + 29.4 \, \text{N} = 98.0 \, \text{N}
\]

### Step 4: Vertical Force Exerted by the Shaft
Since the pulley supports both masses and there are no other vertical forces acting on the system, the vertical force exerted by the shaft to support the system must be equal to the total gravitational force on the masses:
\[
F_{\text{shaft}} = 98.0 \, \text{N}
\]

Thus, the vertical force exerted by the shaft on the pulley is **98.0 N** upward.

Would you like more details or have any questions?

Here are some related questions you may find helpful:
1. What is the effect of pulley mass on the vertical force?
2. How would the tension in the cord change if the masses were equal?
3. What would happen if the pulley were not frictionless?
4. How do you calculate tension in the rope in this scenario?
5. How would the system behave if an external force acted on one of the masses?

**Tip:** Always ensure you account for all forces in a system when determining the force on a support.

Two masses are suspended by a cord that passes over a pulley with negligible mass. The cord also has negligible mass. One of the masses, m1, has a mass of 7.0 kg and the other mass, m2, has a mass of 3.0 kg. The pulley turns on a shaft through the center of the pulley and supports the pulley and all the masses. The vertical force of the shaft on the pulley that supports the whole system is

This problem explores how to determine the vertical force exerted by a shaft on a pulley that supports two masses, 7.0 kg and 3.0 kg. Using Newton's Second Law and force analysis, the solution calculates the total gravitational force and the vertical force required. Ideal for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation