Forces in Connected Systems of Objects Video Lessons

Concept

Problem: An object of mass  m = 0.500 kg is suspended from the ceiling of a truck accelerating at a constant rate on a straight, level road. Taking  a = 3.00 m/s2, find:(a) the angle  θ that the string makes with the vertical(b) the tension  T in the string.

FREE Expert Solution

We're asked to determine the angle θ from the vertical and tension force for a suspended accelerating object.

Anytime we have a problem with multiple objects accelerating together, we know it's a system-of-objects type problem. We'll follow these steps to solve:

1. Draw a free-body diagram for each body we're interested in
2. Write Newton's Second Law equations F=ma, noting that a is the same for both
3. Solve for the target variable

Obviously, we'll be using the equation for Newton's Second Law:

$\overline{)\begin{array}{rcl}\mathbf{\sum }\stackrel{\mathbf{⇀}}{\mathbit{F}}& {\mathbf{=}}& \mathbit{m}\stackrel{\mathbf{⇀}}{\mathbit{a}}\end{array}}$

We may need our equations for decomposing vectors:

And those for determining the magnitude and direction of a force from its components:

$\overline{)\mathbf{|}\stackrel{\mathbf{⇀}}{\mathbit{F}}\mathbf{|}{\mathbf{=}}\sqrt{{{\mathbit{F}}_{\mathbit{x}}}^{\mathbf{2}}\mathbf{+}{{\mathbit{F}}_{\mathbit{y}}}^{\mathbf{2}}}}$

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Problem Details

An object of mass  m = 0.500 kg is suspended from the ceiling of a truck accelerating at a constant rate on a straight, level road. Taking  a = 3.00 m/s2, find:
(a) the angle  θ that the string makes with the vertical
(b) the tension  T in the string.