/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 74 The assembly consists of two blo... [FREE SOLUTION] | 91影视

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Chapter 14: Problem 74

The assembly consists of two blocks \(A\) and \(B\) which have a mass of \(20 \mathrm{~kg}\) and \(30 \mathrm{~kg}\), respectively. Determine the speed of each block when \(B\) descends \(1.5 \mathrm{~m}\). The blocks are released from rest. Neglect the mass of the pulleys and cords.

Short Answer

Expert verified
The speed of both block A and block B when B descends 1.5 m can be found by solving the resulting quadratic equation from the energy conservation law. The velocity will be the same for both blocks due to the connection through the pulley system.

Step by step solution

01

Set up the energy conservation equation

Identify that this is an energy conversion problem where there is a transformation of potential energy into kinetic energy. Specifically, for block B, potential energy is decreasing as it descends 1.5m, while block A is gaining kinetic energy as it moves along with block B. Write down the general form of the energy conservation equation: \( \Delta KE + \Delta PE = 0 \)
02

Substitute known values

Apply the energy conservation law to block B's potential energy and the kinetic energy of both blocks (since both blocks move at the same velocity). Fill in the known values into the equation: \(0.5 \cdot m_A \cdot v^2 + 0.5 \cdot m_B \cdot v^2 - m_B \cdot g \cdot h = 0\). Here, \(m_A\) is the mass of block A (20 kg), \(m_B\) is the mass of block B (30 kg), \(g\) is the acceleration due to gravity (9.8 m/s\(^2\)), \(h\) is the height block B descends (1.5 m), and \(v\) is the velocity we want to find.
03

Solve for the velocity

Rearrange the equation to solve for v. Simplify the equation to obtain the value of the velocity. This might entail first combine similar terms, reorder the equation as needed, and then use a square root operation at the end to solve for v.

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Most popular questions from this chapter

The sports car has a mass of \(2.3 \mathrm{Mg}\) and accelerates at \(6 \mathrm{~m} / \mathrm{s}^{2}\), starting from rest. If the drag resistance on the car due to the wind is \(F_{D}=(10 v) \mathrm{N}\), where \(v\) is the velocity in \(\mathrm{m} / \mathrm{s}\), determine the power supplied to the engine when \(t=5 \mathrm{~s}\). The engine has a running efficiency of \(\varepsilon=0.68\).

The "flying car" is a ride at an amusement park which consists of a car having wheels that roll along a track mounted inside a rotating drum. By design the car cannot fall off the track, however motion of the car is developed by applying the car's brake, thereby gripping the car to the track and allowing it to move with a constant speed of the track, \(v_{t}=3 \mathrm{~m} / \mathrm{s}\). If the rider applies the brake when going from \(B\) to \(A\) and then releases it at the top of the drum, \(A\), so that the car coasts freely down along the track to \(B(\theta=\pi \mathrm{rad})\), determine the speed of the car at \(B\) and the normal reaction which the drum exerts on the car at \(B\). Neglect friction during the motion from \(A\) to \(B .\) The rider and car have a total mass of \(250 \mathrm{~kg}\) and the center of mass of the car and rider moves along a circular path having a radius of \(8 \mathrm{~m}\).

Determine the required height \(h\) of the roller coaster so that when it is essentially at rest at the crest of the hill \(A\) it will reach a speed of \(100 \mathrm{~km} / \mathrm{h}\) when it comes to the bottom \(B\). Also, what should be the minimum radius of curvature \(\rho\) for the track at \(B\) so that the passengers do not experience a normal force greater than \(4 m g=(39.24 m) \mathrm{N}\) ? Neglect the size of the car and passenger.

The 2-Mg car increases its speed uniformly from rest to \(25 \mathrm{~m} / \mathrm{s}\) in \(30 \mathrm{~s}\) up the inclined road. Determine the maximum power that must be supplied by the engine, which operates with an efficiency of \(\varepsilon=0.8 .\) Also, find the average power supplied by the engine.

As indicated by the derivation, the principle of work and energy is valid for observers in any inertial reference frame. Show that this is so, by considering the \(10-\mathrm{kg}\) block which rests on the smooth surface and is subjected to a horizontal force of \(6 \mathrm{~N}\). If observer \(A\) is in a fixed frame \(x\), determine the final speed of the block if it has an initial speed of \(5 \mathrm{~m} / \mathrm{s}\) and travels \(10 \mathrm{~m}\), both directed to the right and measured from the fixed frame. Compare the result with that obtained by an observer \(B\), attached to the \(x^{\prime}\) axis and moving at a constant velocity of \(2 \mathrm{~m} / \mathrm{s}\) relative to \(A\). Hint: The distance the block travels will first have to be computed for observer \(B\) before applying the principle of work and energy.
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