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Learning Introductory Physics with Activities

Paul J. Emigh, Rebecka Tumblin, Kathryn Hadley, Danielle Skinner

Section 5.6 Practice - Systems

Subsection Practice

Explanation 5.6.1. Two Books in an Elevator.

The two books below are in an elevator that is moving downward. As the elevator approaches the ground floor, its speed decreases. Identify and rank all forces acting on the two books by magnitude, from largest to smallest.
Figure 5.6.1. Two books in an elevator.
Tip.
Free-body diagrams can be very helpful! Your reasoning should specifically reference how you used Newton’s Laws.

A*R*C*S 5.6.2. The Action Movie Star and the Helicopter.

An action movie star is standing on a heavy industrial crate lifted upward by a helicopter. Assume you know all masses and the tension in the cable connected to the crate. Determine the acceleration of the crate and the movie star.
Solution.

A*R*C*S 5.6.3. Stacked Blocks.

The blocks below have different masses, \(m_1\) and \(m_2\text{.}\) Each block is connected to a horizontal rope; the upper rope is connected to the wall and the lower rope is being pulled to the right with known tension \(T\text{.}\) All coefficients of kinetic friction \(\mu_k\) between all surfaces are equal and nonzero. Determine the tension in the upper rope and the acceleration of the lower block.
Figure 5.6.2. Two blocks attached to ropes.

Calculation 5.6.4. Angled ramp with a pulley.

A box with \(m_1 = 10.5 \mathrm{~kg}\) is on an inclined plane with negligible friction between the box and the incline. This box is attached via an ideal string and pulley to a hanging mass with \(m_2 = 5.5 \mathrm{~kg}\text{,}\) as shown. The incline makes an angle of 20.0° with respect to the horizontal. Use \(g = 10 \mathrm{~m/s^2}\text{.}\) Rank the magnitude of accelerations for \(m_1\) and \(m_2\text{.}\) Do you necessarily know the direction of acceleration of \(m_1\) without doing any calculations? Find the magnitude of acceleration for \(m_1\text{.}\) What direction is the acceleration of \(m_1\text{?}\)
Figure 5.6.3.
Answer 1.
\(|\vec{a}_1| = |\vec{a}_2|\)
Answer 2.
No, but you can just guess a direction. For example, if you assume \(m_1\) accelerates up the ramp but our analysis results in a negative acceleration for \(m_1\text{,}\) that means you picked the wrong direction, but the magnitude of your result is correct.
Answer 3.
\(1.19 \mathrm{~m/s^2}\)
Answer 4.
Up the incline.

References References

[1]
Practice activities provided by BoxSand: https://boxsand.physics.oregonstate.edu/welcome.
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