Classical Mechanics Answers

1.Water flows at 750 m³/s down a rectangular channel made of finished concrete. The channel has a width of 4 m and a downward slope of 0.0002, and the water depth is 1.5 m at the control section A. Determine the distance x from A to where the depth becomes 1.25 m. Use delta y = 0.05 m and plot the surface profile. Take n = 0.012.

2. The rectangular channel is fitted with a 60 degrees or triangular weir plate. If the upstream depth of the water is 2 m. and the bottom of the weir plate is 1.6 m from the bottom of the channel. determine the volumetric flow of water prang over the weir. Take C_d = 0.72. 

1. The culvert is at a downward slope S₀. Determine the depth y of water that will produce the maximum volumetric flow.

2.The channel is made of unfinished concrete and has a downward slope of 0.006. Determine the volumetric flow if the depth is y = 3 m. Take n = 0.014.

1.The rectangular channel has a width of 4 m and transports water at 1.20(10⁶) liters/min. If the elevation of the bed drops by 0.4 ft, determine the depth y₂ after the depression.

2. A flow of 60 m³/s passes under the sluice gate. If y₁ = 6 in. determine the depth y₂ and the type of flow downstream. Also, what is the maximum volumetric flow that can pass through the gate?

1.A large tank contains water having a depth of 1.5 m. lf the tank is on an elevator that is descending, determine the horizontal speed of a wave created on its surface if the rate of descent is (a) constant at 6 m/s. (b) accelerated at 1.5 m/s2. (c) accelerated at 9.81 m/s2.

2.. Water flows at 840(103) liters/min through a rectangular channel having a width of 3 m. If yA = 1 m, show that yB = 1.25 m is possible. What is the necessary increase in elevation h of the channel bed to create this depth?

a grain retailer puts a 1000 kg lead block under the platform of this scale. by how much does this increase the reading of the scale when 50kg sack of rice is on top of its platform, if the distance between their centers are .03 meter apart

A thin spherical shell of mass M = 3.00 [kg] and radius R = 1.50 [m] compresses a spring (k = 500. [N/m]) by 0.400 [m]. After releasing the shell from rest, it rolls without slipping along the floor and up a surface inclined at an angle θ = 30.0◦, as shown in the figure. What is the angular speed of the shell when it reaches a distance L = 2.00 [m] from the base of the incline? (I = 2/3mr^2)

the loaded roller coaster has a mass of 2500 kg. the starting point of the run is 22m above point A; the run from B to C is 120m long; the run from C to D is 100m. at D, brakes are applied, bringing the coaster to a halt 15m further along a E. if the friction from B to D is 0, find

(a) the potential energy of the roller coaster at the starting point

(b) KE of the roller coaster at C

(c) the speed of the roller coaster at D; the average braking force applied between D and E

A pendulum has a mass of 2.35 kg. If the pendulum swings back and forth 110 times in 90.0 seconds, what is the length of the pendulum

the loaded roller coaster has a mass of 2500 kg. the starting point of the run is 22m above point A; the run from B to C is 120m long; the run from C to D is 100m. at D, brakes are applied, bringing the coaster to a halt 15m further along a E. if the friction from B to D is 0, find

(a) the potential energy of the roller coaster at the starting point

(b) KE of the roller coaster at C

(c) the speed of the roller coaster at D; the average braking force applied between D and E

what is the orbit radius of a 300kg satellite that completes one circular orbit around the earth every 3.6hr?