A block of mass m_1 is connected by a string over a pulley to a block of mass m_2 that is sliding on a flat table. The string is light and does not stretch; the pulley is light and turns without friction. The coefficient of friction between the sliding block and the table is μ. A force F is also applied to m_1 at an angel of θ° with the horizontal:

Question

A block of mass m_1 is connected by a string over a pulley to a block of mass m_2 that is sliding on a flat table. The string is light and does not stretch; the pulley is light and turns without friction. The coefficient of friction between the sliding block and the table is μ. A force F is also applied to m_1 at an angel of θ° with the horizontal:

i) Find the tension of the box.
ii) what is the change in each block's velocity over a 2 second interval?

I found that the blocks' acceleration is a=(-m_1gsinθ-m_2gcosθ)/(m_1+m_2)

Answer 1

To find the tension of the string, we need to consider the forces acting on each block separately and use the Newton's laws of motion. Let's analyze the forces on each block:

For the block of mass m1:
1. The force F applied at an angle θ° with the horizontal.
2. The weight of the block, which acts vertically downward and has a magnitude of m1g, where g is the acceleration due to gravity.
3. The tension in the string, which acts vertically upward.

For the block of mass m2:
1. The weight of the block, which acts vertically downward and has a magnitude of m2g.
2. The frictional force, which acts in the opposite direction of motion and has a magnitude of μN, where N is the normal force exerted on the block by the table.
3. The tension in the string, which acts vertically upward.

Now, let's resolve the forces along the vertical direction for each block:

For the block of mass m1:
Net force = ma1 = T - m1g*cosθ

For the block of mass m2:
Net force = ma2 = m2g - μN = m2g - μ(m2g + T) = m2g - μm2g - μT

Since the tension in the string is the same for both blocks, we can equate the equations for net force along the vertical direction:

T - m1g*cosθ = m2g - μm2g - μT

Now, we can solve this equation to find the tension T.

For the second part of the question:
The blocks' acceleration, a, is already given as a = (-m1gsinθ - m2gcosθ)/(m1 + m2). To find the change in velocity for each block over a 2-second interval, we can use the kinematic equation:

Δv = a * Δt

Here, Δv is the change in velocity, a is the acceleration, and Δt is the time interval. Substitute the given values to find the change in velocity for each block.