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A thin rod L meters long has a linera density that varies as \(\rho (x) = \rho_{0} e^{-ax}\). Find
a) the mass of the rod
b) the center of mass
c) the rotational inertia about an axis perpendicular to the rod passing through the end at x = 0
A rope exerts a constant horizontal force of 250N to pull a 60 Kg crate across the floor.
small object is placed to the left of a convex lens and on the optical axis. What is the position of the image formed by the lens
A beam contains 4.0 108 doubly charged positive ions per cubic centimeter, all of which are moving north with a speed of 1.3 105 m/s
A sprinter explodes out of the starting block with an acceleration of +3.5 m/s2, which she sustains for 1.0 s. What is her velocity at the end of the race
When a 5.5 cm long pencil is arranged perpendicular to a convex mirror's optical axis at a distance of 29 cm from the mirror, its image is 2.8 cm tall. (a) What is the mirror's focal length (include sign if negative)? (b) How tall is the pencil's ..
While moving down the track at 10.0 m/s, you uniformly accelerate to 32.0 m/s in 10 s. Illustrate what is the average net force that you have applied to the car during the 10 s interval?
A spring with spring constant 19 hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 2.5 and released. The ball makes 33 oscillations in 15 seconds. What is its utmost speed.
A 6.4 cm diameter pipe gradually narrows to 4.0 cm. When water flows through this pipe at a certain rate, What is the volume rate of flow
An audio amplifier provides an alternating rms potential difference of 15.0V. A loudspeaker connected to the amplifier has a resistance of 10.4 ohm. what is the rms current in the speaker
A 0.35kg mass suspended from a spring moves with simple harmonic motion. At the instant mass is displaced from equilibrium by -0.105 m, what is its acceleration? (The spring constant is 11.8N/m)
A irregular piece of metal has a dry mass of 5.7 kg. Once it is submerged it has an apparent mass of 2.4 kg. What is the density of the piece of metal
A 17g rifle bullet travelling 220 m/s buries itself in a 3.90 kg pendulum hanging on a 3m long string, which makes the pendulum swing upward in an arc. Find out the vertical and horizontal components of the pendulum's displacement.
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