Question

physics problem pulley system 50 kg mass

Answer 1

Sure! Let's work through a typical physics problem involving a pulley system with a 50 kg mass.

### Problem Statement:

A 50 kg mass is hanging from a pulley system. The pulley is frictionless, and the mass is connected to another mass on a frictionless surface.

1. If the system is released from rest, what will be the acceleration of the 50 kg mass?
2. If there is a second mass, say 30 kg, on the frictionless surface, what is the acceleration of both masses?

### Given:
- Mass of the hanging object, \( m_1 = 50 \, \text{kg} \)
- Mass on the surface, \( m_2 = 30 \, \text{kg} \)
- Acceleration due to gravity, \( g = 9.81 \, \text{m/s}^2 \)

### Solution:

1. **Determine the forces acting on the masses:**

For the hanging mass \( m_1 \):
- The force of gravity acting downwards:
\[
F_{\text{gravity}} = m_1 \cdot g = 50 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 = 490.5 \, \text{N}
\]

For the mass on the surface \( m_2 \):
- There is no gravitational force acting downward for horizontal movement, but it will experience tension in the string \( T \) acting towards the pulley.

2. **Newton's Second Law for each mass:**

For the hanging mass \( m_1 \):
\[
m_1 g - T = m_1 a \tag{1}
\]

For the mass on the surface \( m_2 \):
\[
T = m_2 a \tag{2}
\]

3. **Set up equations:**

From \( (2) \):
\[
T = 30a
\]

Substituting \( T \) in \( (1) \):
\[
50g - 30a = 50a
\]

Rearranging gives:
\[
50g = 80a \implies a = \frac{50g}{80}
\]

4. **Calculate acceleration \( a \):**
\[
a = \frac{50 \cdot 9.81}{80} = \frac{490.5}{80} \approx 6.13 \, \text{m/s}^2
\]

5. **Determine the tension \( T \):**
Using \( T = m_2 a \):
\[
T = 30 \cdot 6.13 \approx 183.9 \, \text{N}
\]

### Summary of Results:
- The acceleration of the system is approximately \( 6.13 \, \text{m/s}^2 \).
- The tension in the string is approximately \( 183.9 \, \text{N} \).

Feel free to ask if you have a different scenario in mind or need further assistance!