When a .22-caliber rifle is fired, the expanding gas from the burning gunpowder creates a pressure behind the bullet. This pressure causes the force that pushes the bullet through the barrel. Suppose the barrel has a length of 0.557 m and an opening whose radius is 2.94 x 10-3 m. A bullet (mass = 2.6 x 10-3 kg) has a speed of 467 m/s after passing through this barrel. Ignore friction and determine the average pressure of the expanding gas.

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A cylindrical tank, shown in the figure, has height 8 m and radius 4 m. Suppose the water tank is half-full of water. Determine the work required to empty the tank by pumping the water to a level 6 m above the top of the tank. Use 1000 kg/m³ for the density of water and 9.8 m/s² for the acceleration due to gravity. 4 m Draw a y-axis in the vertical direction (parallel to gravity) and choose the center of the bottom of the tank as the origin. For 0 ≤ y ≤8, find the cross-sectional area A(y). A(y) = (Type an exact answer, using as needed.) 8 m

A block of mass 12 kg slides down a frictionless inclined plane inclined at 35° with no initial velocity and is stopped by a spring of k= 3.0 * 10^4 N/m. The block slides a total distance of d = 3 m from the point where it was released to the point where it stops due to the resistance of the spring. How much is the spring compressed when the block stops?

What does the percent difference between GPE and KE tell you about the Efficiency of energy transformations in this experiment ?

An object of mass 6.25 kg slides down a hill of height 21.1 m. At the bottom of the hill is a spring with spring constant 53.6 N/m. How far is the spring compressed when the mass comes to rest? Assume the mass starts from rest at the top of the hill. Give your answer in meters to three significant figures.

5. A cart with m= 3.40kg rides on the track shown. The track is frictionless except for a level section 0.40m long where μk = 0.54. The cart is initially at rest against spring 1 (k₁ = 1400N/m) which is compressed by 8.00cm. When released it travels along the track until it reaches spring 2 (k2= 800N/m) which it compresses until the cart stops. If h₁ = 0.38m and h₂ = 0.14m, determine the speed of the cart at points A, B, C and D. Also how much will spring 2 be compressed at the end. framm] =3.40kg kží = 800 N/m Remb A k₁=1 2₁-1400/m h₁-0,38 D B d=0.40m = 0,54 мк of ....... oservation Im h₂= = 0,14