Balanced Contact Forces

Pulled in two Different Directions.

Part A: In the diagram, the box (m_1) is moving to the right with a constant velocity (v). Express the magnitude of F_2 in terms of F_1, Θ, Φ, μ and any physical constants as necessary. F_1 and F_2 are both being applied by lightweight strings attached to m_1.

Part B: Suppose the magnitude of F_2 was the maximum the force able be applied before breaking the string. Outline how the box, m_1, could be made to accelerate to the right without increasing the magnitude of the force being applied by F_2. Support your answer with your expression from part A.

Part C: Suppose the magnitude of F_1 were to increase, while remaining at the same angle. Outline two possible outcomes to the scenario.

Motion upon release

Initially each of the masses, the black dot, shown below are held in place by and external force of unknown origin. Upon removal of the external force of unknown origin, the system is allowed to move freely. In each of the scenarios below, determine the initial magnitude and direction of acceleration of the mass. The scale of the grid: 1 square = 1 Newton

m = 2 kg

ΣF_horizontal = 0 N ΣF_vertical = 0 N

∴ a = 0 m/s/s (forces are balanced)

m = 3 kg

ΣF_horizontal = 0 N ΣF_vertical = 0 N

∴ a = 0 m/s/s (forces are balanced)

m = 5 kg

ΣF_horizontal = -5 N ΣF_vertical = 0 N

∴ a = -1 m/s/s (to the left)

m = 6.5 kg

ΣF_horizontal = 13 N to the right

ΣF_vertical = 0 N

∴ a = 2 m/s/s to the right

Comparison of Accelerations

In each of the pairs of scenarios, compare the acceleration of the blocks in terms of given variables and any necessary physical constants as needed.

Scenario A:

Which of the two blocks do you think will have the greatest acceleration?
Express the minimum force necessary to start the block moving in terms of μ_s, F_A, m_1 and any physical constants as necessary.
Compare the acceleration of A to B after they have begun to move.

Scenario B:

Scenario C:

Express the minimum force necessary to start the block moving in terms of μ_s, F_A, m_1 and any physical constants as necessary.
Compare the acceleration of C to D after they have begun to move.
Which of the four scenarios will have the greatest acceleration after it has begun to move?

Scenario D:

Pairs of Blocks

Additional Resources:

The Addition of a Frictional Force:

A pair of blocks made of the same material is being pulled to the right at a constant velocity as shown to the right. Express the tension in T_1 in terms of m_1, m_2, μ_k and any physical constants as necessary.

Frictional Forces and Acceleration:

The student conducting the experiment then doubled the force acting in T_1, causing the system to accelerate. Express the tension of T_2 while the 2-block system is accelerating.

Page updated

Google Sites

Report abuse