1. (a) A tube of fluid is shown in the diagram below. There is a hole on the side through which the fluid is pouring out. The hole has an area A. The mouth of the tube has an area 3A. The fluid is currently at a height H while the hole is at height h. Find an expression for the velocity of the fluid leaving the hole.



(b) A hollow glass cubic box has mass m_box = 0.250 kg. The box has sides of length L = 15.0 cm. The sides of the glass box are very thin. The inside of the box is filled to a height h with water then sealed. The box is then submerged in water and it is observed that the box will stay at any desired level provided that the box is not tipped. The box is said to have neutral buoyancy. Find the height h of the water in the box. The densities of air and water are 1.3 kg/m³ and 1000 kg/m³ respectively.



2. The diagram below shows a toy car being travelling at speed v crashes into an ideal spring of spring constant K. All four car wheels roll without slipping. Find the distance L that the toy compresses the spring. The toy car wheels are solid cylindrical disks, each having mass m_w. The body of the toy car has mass M.



3. A flat square plate of mass 15.0 kg and width 0.90 m is rotating clockwise about a fixed axle at 20 rad/s as shown on the left below. On the same axle, but above the plate and rotating independently, is the object shown in the middle diagram below. It consists of two flat uniform disks joined at their edge. The mass of the total object is 10.0 kg. The radius of each disk is 0.30 m. The object is rotating counterclockwise at 13 rad/s. The object is allowed to drop onto the plate. After some slipping and sliding, the two start rotating at the same rate as shown in the diagram at the right.
   (a) Find the direction and rate at which the objects rotate.
   (b) How much energy is lost to the slipping and sliding?



4. The diagram below shows three blocks on a frictionless tabletop. The upper block has a mass M₁ and is pulled to the right by a horizontal force F₁. The bottom block has a mass M₂ and is pulled to the left with a horizontal force F₂. The middle block has a mass M₃. The coefficients of friction between the upper and middle blocks are μ_s13 and m _k13. The coefficients of friction between the middle and lower blocks are μ_s32 and m _k32. All the blocks slide. Determine the equations needed to find the acceleration of each block. (Do not solve the equations!)

   

5. A gardener is rolling a heavy solid cylinder over newly laid sod to flatten it as shown in the diagram below. The gardener is pushing the cylinder with a force F = 110 N at an angle q = 40.0° through the axle. What is the acceleration of the roller? The roller has a mass of 90.0 kg and a radius of 18.0 cm.

   

6. A weird sign is hanging from the side of a building as shown in the diagram below. The radius of the big circle is R. The radius of the small circle is ½R. The sign is uniform and has a mass of 120 kg. The cable is attached to the top of the left small circle. The hinge is attached to the rightmost side of the right small circle. The cable makes an angle of 60° with the wall.
   (a) Find the tension in the supporting cable.
   (b) Find the horizontal and vertical components of the hinge force.

   

7. (a) A block of mass 5.00 kg is attached to a spring of constant K = 2000 N/m. The spring is compressed 0.20 m and released. As the block returns toward equilibrium passing through x = - ½A, you start your graphing equipment with this instant as t = 0. What is the exact (i.e with numbers) equation of the plot? The surface is frictionless.

   

   (b) The diagram below shows two speakers, S1 and S2, producing the same frequency sound and a detector D which are underwater. The speed of sound in water is 1497 m/s. The detector is only sensitive to frequencies between 10,000 and 21,000 Hz. Find the lowest frequency in that range for which there is destructive interference.

   

8. (a) A fire engine of with a siren blaring at 800 Hz and travelling at an unknown speed is approaching you. You are not moving. You pull out your lucky 800 Hz tuning fork and ring it. You hear a beat frequency of 20 Hz. What frequency do you hear for the approaching fire engine siren? How fast is the fire engine moving? The speed of sound in air is 340 m/s.

   (b) You are the same distance from each of you stereo speakers. With the stereo turned off, the sound level is 56 dB. With the stereo on using both speakers the sound level is 75 dB. If you adjusted your stereo to turn one speaker off, what would the sound level be then?

9. Two blocks are connected by string run around a set of pulleys as shown in the diagram below. The masses of the blocks are M₁ and M₂. The pulleys are identical thin hoops of mass m. Derive the equations for finding the acceleration of the blocks. Do no solve the equations!

   

Questions? mike.coombes@kwantlen.ca