Two blocks connected by a string are pulled across frictionless surface by a force applied to one of the blocks, as shown below. If each block has an acceleration of 2.0 m/s? to the right.(a) Label all forces acting on A and B. What is the magnitude of F of the applied force?
The Correct Answer and Explanation is :
To solve this problem, let’s define the forces acting on each block and determine the magnitude of the applied force.
Forces Acting on Each Block
We assume:
- Block A has mass ( m_A )
- Block B has mass ( m_B )
- The tension in the string is ( T )
- The applied force is ( F ), acting on Block A
- The acceleration of both blocks is 2.0 m/s² to the right
- The surface is frictionless, so no resistive forces act
The forces acting on each block:
- Block A:
- The applied force ( F ) pulls to the right.
- The tension ( T ) in the string pulls to the left.
- The normal force ( N_A ) from the surface acts upward.
- The gravitational force ( m_A g ) acts downward.
- Block B:
- The tension ( T ) in the string pulls it to the right.
- The normal force ( N_B ) from the surface acts upward.
- The gravitational force ( m_B g ) acts downward.
Since there is no vertical movement, the normal forces and gravitational forces cancel out, leaving only the horizontal forces to consider.
Calculating the Applied Force ( F )
Using Newton’s Second Law:
For Block B (only tension provides acceleration):
[
T = m_B a
]
For Block A (net force is ( F – T )):
[
F – T = m_A a
]
Substituting ( T = m_B a ) into the equation:
[
F – m_B a = m_A a
]
[
F = (m_A + m_B) a
]
Given ( a = 2.0 ) m/s², we can substitute the given masses to find ( F ).
Now, I will generate the image of the system.
Here is the generated image showing the forces acting on the two blocks. It includes labeled forces such as the applied force ( F ), tension ( T ), normal forces ( N_A ) and ( N_B ), and gravitational forces ( m_A g ) and ( m_B g ).
Let me know if you need further clarification or additional modifications!