connected by a string as shown. Mass mA= 4.0 kg rests on a fri what will be the resulting acceleration of the masses? (b) If the masses were in hile mв= 5.0 kg is initially held at a height of h=0.75 m above the floor. (a) If kinematic equations to find their velocity just before mв hits the floor. £ O
Gravitational force
In nature, every object is attracted by every other object. This phenomenon is called gravity. The force associated with gravity is called gravitational force. The gravitational force is the weakest force that exists in nature. The gravitational force is always attractive.
Acceleration Due to Gravity
In fundamental physics, gravity or gravitational force is the universal attractive force acting between all the matters that exist or exhibit. It is the weakest known force. Therefore no internal changes in an object occurs due to this force. On the other hand, it has control over the trajectories of bodies in the solar system and in the universe due to its vast scope and universal action. The free fall of objects on Earth and the motions of celestial bodies, according to Newton, are both determined by the same force. It was Newton who put forward that the moon is held by a strong attractive force exerted by the Earth which makes it revolve in a straight line. He was sure that this force is similar to the downward force which Earth exerts on all the objects on it.
![**Problem 3:**
Two masses are connected by a string as shown. Mass \( m_A = 4.0 \, \text{kg} \) rests on a frictionless inclined plane, while \( m_B = 5.0 \, \text{kg} \) is initially held at a height of \( h = 0.75 \, \text{m} \) above the floor.
1. **(a)** If \( m_B \) is allowed to fall, what will be the resulting acceleration of the masses?
2. **(b)** If the masses were initially at rest, use the kinematic equations to find their velocity just before \( m_B \) hits the floor.
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### Free Body Diagram and Force Components Explanation
The provided diagram shows mass \( m_A \) resting on an inclined plane at an angle \( \theta = 32^\circ \). The gravitational force acting on \( m_A \) has components along the plane (\( mg \sin \theta \)) and perpendicular to the plane (\( mg \cos \theta \)). Mass \( m_B \) is hanging vertically with a downward force due to gravity of \( mg \).
### Calculations for Part (a):
1. **Resulting Acceleration of the Masses**:
- The net force (\( F \)) acting on the system is given by the difference in forces due to the masses:
\[
F = m_B g - m_A g \sin \theta
\]
- The total mass (\( m_{\text{total}} \)) of the system is:
\[
m_{\text{total}} = m_A + m_B = 4 \, \text{kg} + 5 \, \text{kg} = 9 \, \text{kg}
\]
- The acceleration \( a \) of the system is:
\[
a = \frac{F}{m_{\text{total}}}
\]
- Substituting the values:
\[
a = \frac{(m_B - m_A \sin \theta) g}{m_A + m_B}
\]
- Therefore, the acceleration is:
\[
a = \frac{(5 \, \text{kg} - 4 \, \text{kg} \cdot \sin(32^\circ](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd3a80bdb-dbe3-4058-9ea9-0990b19198fe%2F6e657dd8-4bf4-4803-be0d-971f09217724%2Fbtwhu1n_processed.jpeg&w=3840&q=75)
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