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A cylindrical pipe, closed at both ends, contains air molecules, where the speed of sound is [v] m/s. When the pipe resonates, it forms a standing sound wave inside. The figure shows a snapshot of the standing wave with a wavelength of [lamda] m. When the air in the pipe resonates at its fundamental frequency, calculate the fundamental frequency in hertz (Hz).

The figure shows a top view of a 50 kg horizontal uniform disk with a radius of 2 m that can rotate about a vertical axis through its center. The disk is initially at rest. A 20 kg point mass is moving at a speed of 30 m/s along a path that is tangent to the rim of the disk. At a certain moment, the point mass contacts the rim at point P and becomes attached to the disk. Determine the linear (tangential) speed of the point mass immediately after it becomes attached. Express your answer in m/s.

Box A with mass 2 kg, initially moving along a straight line with a velocity of +5 m/s, experiences an impulse due to an external force. The graph below shows the magnitude of the force applied to the box as a function of time. F2 = 100 N, F3 = 40 N, t2 = 0.2 s, and t3 = 0.5 s. Determine the final speed of the box after the force has been applied. Express your answer in meters per second (m/s).

Objects A and B are made of the same material with a density of [rho1] kg/m³. Object A is fully submerged in an unknown liquid, and object B is placed on top of A such that only a fraction [f] of object B is submerged. Given that the density of the unknown liquid is [rho2] kg/m³ and the volume of object B is [vB] m3, determine the volume (in m³) of object A.

A string is stretched between two fixed points, producing transverse waves when plucked. The string has a length of 8 m and a mass of [m] kg. The figure displays a segment of the wave along the x-y plane at t = 0. A = 0.5 m and x3= [x3] m. If the string oscillates at a frequency of [f] Hz, determine the tension in the string in newtons. [Hint: the wavelength can be determined from the x-y graph.]

A frictionless pulley has the shape of a uniform solid disk with a mass of 4 kg and a radius of 0.2 m. A box of mass 4 kg is attached to a very light string that is wrapped around the rim of the pulley. The system is released from rest. Determine the magnitude of the linear acceleration of the box in m/s².

A 0.45 kg mass is resting on a vertically oscillating platform. The platform undergoes simple harmonic motion. The displacement-time graph of the platform’s motion is shown in the figure. t2= [t2] s. Determine the maximum oscillation amplitude that allows the mass to stay in contact with the platform at all times. [Hint: the supporting (normal) force becomes zero when the mass is about to lose contact with the platform. Consider that the maximum force in SHM is Fmax = m × amax.]

An enclosed container is filled with an unknown gas, an unknown liquid, and water. h1= [h1] m and h2 = [h2] m. Given that the density of the unknown liquid is 780 kg/m³, the density of water is 1000 kg/m³, and the pressure of the gas is Pgas = [Pgas] × 104 Pa, determine the pressure at the bottom of the container in Pa.

What emotion primarily drove Douglass’s desire to learn how to read?