PHYS 2421 EXAM #4 Monday, 26 October 2015 NAME ______________________________________

Work two (2) of the following problems from Chapter 9:

87) A ball having a mass of 150g strikes a wall with a speed of 5.2 m/s and rebounds with only 50% of its initial kinetic energy. (a) What is the speed of the ball immediately after rebounding? (b) What is the magnitude of the impulse on the wall from the ball? (c) If the ball is in contact with the wall for 7.6 ms, what is the magnitude of the average force on the ball from the wall during this time interval?

(Hints: (a) Use 0.50*K = ½ mv2 to find velocity, (b) J = m1 v1 to find impulse, (c) Fave = J/t ) 111) A 2900 kg rocket sled moves at 250 m/s on a set of rails. At a certain point, a scoop on the sled dips into a trough of water located between the tracks and scoops water into an empty tank on the sled. By applying the principle of conservation of linear momentum determine the speed of the sled after 920 kg of water has been scooped up. Ignore any retarding force on the scoop. (Hints: 𝑚𝑠𝑣𝑖 = (𝑚𝑠 + 𝑚𝑤)𝑣𝑓, and solve for vf.)

117) A collision occurs between a 2.00 kg particle traveling with velocity �⃗� = (−4.00 𝑚/𝑠)𝑖̂ + (−5.00 𝑚/𝑠)𝑗 and a 4.00 kg particle traveling with velocity�⃗� = (6.00 𝑚/𝑠)𝑖̂ + (−2.00 𝑚/𝑠)𝑗 . The collision of the two particles connects them. What then is their velocity in (a) unit-vector notation and as a (b) magnitude and (c) angle?

(Hints: Eqn. 9-53 where 𝑉 =𝑚1

𝑚1+𝑚2𝑣1𝑖 is used when a collision is inelastic, then use 𝑚1𝑣1⃗⃗⃗⃗⃗ + 𝑚2𝑣2⃗⃗⃗⃗⃗ = (𝑚1 + 𝑚2)�⃗⃗�.)

125) An atomic nucleus at rest at the origin of an xy coordinate system transforms into three particles. Particle 1, mass 16.7 X 10-27 kg, moves away from the origin at velocity (6.00 X 106 m/s) 𝑖̂, particle 2, mass 8.35 X 10-27kg, moves away at velocity (-8.00 X 106 m/s) 𝑗̂. (a) In unit-vector notation, what is the linear momentum of the third particle, mass 11.7 X 10-27 kg? (b) How much kinetic energy appears in this transformation? (Hints: Use momentum conservation, p3 = p1 – p2 and kinetic energy conservation, KE = ½ mv3

2 + ½ mv22+ ½ mv1

2.) Work two (2) of the following problems from Chapter 10:

70) A wheel, starting from rest, rotates with a constant angular acceleration of 2.00 rad/s2. During a certain 3.00 s interval, it turns through 90.0 rad. (a) What is the angular velocity of the wheel at the start of the 3.00 s interval? (b) How long has the wheel been turning before the start of the 3.00 s interval?

(Hints: (b) use ∆𝜃 = 𝜔1∆𝑡 + 1/2𝛼(∆𝑡)2 to find 1, substitute into Eq. 10-12,𝜔1 = 𝜔0 + 𝛼𝑡 to find t and then find 1.)

76) Starting from rest at t =0, a wheel undergoes a constant angular acceleration. When t = 2.0 s, the angular velocity of the wheel is 5.0 rad/s. The acceleration continues until t = 20 s, when it abruptly ceases. Through what angle does the wheel rotate in the interval t = 0 to t = 40s? (Hints: (a) Eq. 10-12. 𝜔 = 𝜔0 + 𝛼𝑡, to find angular acceleration, (b) Eq. 10-13, 𝜃 = 𝜃0 + 𝜔0𝑡 + 1/2𝛼𝑡2 angular displacement.)

92) Our Sun is 2.3 X 104 ly (light-years) from the center of our Milky Way galaxy and is moving in a circle around that center at a speed of 250 km/s. (a) How long does it take the Sun to make one revolution about the galactic center? (b) How many revolutions has the Sun completed since it was formed about 4.5 X 109 years ago?

(Hints: T = 2R/v. )

107) A pulley wheel that is 8.0 cm in diameter has a 5.6 m long cord wrapped around its periphery. Starting from rest, the wheel is given a constant angular acceleration of 2.5 rad/s2. (a) Through what angel must the wheel turnfor the cord to unwind completely? (b) How long will this take? (Hints: (𝑎)∆𝜃 = 𝜔1∆𝑡, (𝑏)𝜃 = 1/2𝛼𝑡2)

PHYS 2421 EXAM #4 Monday, 26 October 2015 NAME ______________________________________

Work two (2) of the following problems from Chapter 11: 28. A 2.0 kg particle-like object moves in a plane with velocity components v x = 30 m/s and vy = 60 m/s as it passes through the point with (x, y) coordinates of (3.0,-4.0)m. Just then in unit-vector notation, what is its angular momentum relative to (a) the origin and (b) the point located at (-2.0,-2.0)m?

(Hints: 𝑙 = 𝑟 × �⃗� for both position vectors)

68. A top spins at 30 rev/s about an axis that makes an angle of 30 degree with the vertical. The mass of the top is 0.50 kg, its rotational inertia about its central axis is 5.0 X 10-4 kg m2, and its center of mass is 4.0 cm from the pivot point. If the spin is clockwise from an overhead view, what are the (a) precession rate and (b) direction of the precession as viewed from overhead?

(Hints: Use Eqn. 11-46, Ω =𝑀𝑔𝑟

𝐼𝜔⁄ )

72. A thin-walled pipe rolls along the floor. What is the ratio of its translational kinetic energy to its rotational kinetic energy about the central axis parallel to its length?

(Hints: 𝐾 =1

2𝐼𝜔2, 𝑤ℎ𝑒𝑟𝑒 𝐼 = 𝑚𝑅2, 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 𝐾𝑡𝑟𝑎𝑛𝑠𝑙/𝐾𝑟𝑜𝑡)

76. A uniform slab of granite in the shape of a block has face dimensions of 20cm and 15 cm and a thickness of 1.2 cm. The density of granite is 2.64 g/cm3. The slab rotates around an axis that is perpendicular to its face and halfway between the center and a corner. Its angular momentum about that axis is 0.104 kg m2/s. What is its rotational kinetic energy about that axis?

(Hints: Use Item (i) in Table 10.2 gives the moment of inertia about the center of mass in terms of width a (0.15 m) and

length b (0.20 m). The distance from the com to the point about which the slab spins is given by √(𝑎4⁄ )2 + (𝑏

4⁄ )2 . where

the volume of the slab is abh, the kinetic energy will be K = ½ L 2/I.)