PHYSICS 121 HOMEWORK for EXAM # 3

Assignment #19 Section 7-1 Date Due: Tue. Feb. 18
Assignment #20 Section 7-2 Date Due: Wed. Feb. 19
Assignment #21 Sections 8-4 & 8-6 Date Due: Fri. Feb. 21
Assignment #22 Section 8-6 Date Due: Mon. Feb. 24
Assignment #23 Section 8-6 Date Due: Tue. Feb. 25
Assignment #24 Section 8-7 Skip- Not Required

START for EXAM #3 CHAPTER 7
Assignment #19 Section 7-1 Date Due: Tue. Feb. 18
19. A 48.0 kg block slides along the frictionless surface of a hill that is 188 m high with an initial speed 19.0 m/s {23.0 m/s}. Relative to the bottom of the hill: (Conservation of Energy)
(A) what is the block's initial potential energy relative to the bottom of the hill as it starts down the hill?
(B) what is the block's initial mechanical energy as it starts down the hill ?
Ans:{101 kJ}
(C) what is the block's mechanical energy when the block is 75.0 m above the bottom of the hill?
Ans:{?}
(D) what is the block's speed when the block is 75.0 m above the bottom of the hill?
Ans:{52.4 m/s}
(E) what is the block's height above the bottom of the hill when its speed is 61.0 m/s ?
Ans:{25.1 m}
BONUS:
(F) At what height will the block's kinetic energy be equal to 2.5 times its potential energy ?
Ans:{61.4 m}

Assignment #20 Section 7-2 Date Due: Wed. Feb. 19
20. A 1.70 kg block, initially at rest, is connected to an unstreached spring with a spring constant of 350 N/m. The block rests on rough horizontal surface with a coefficient of kinetic friction equal to .440. The block is pulled to the right by a 45.0 N constant force.
(A) Which of the following forces are non-conservative forces ?
a. The force that the spring exerts on the block, Fs.
b. The force of friction acting on the block, Ff.
c. The constant force applied to the block, Fapp.
(B) When the block has moved 16.2 cm {7.40 cm}, determine:
a. The work done by the applied force, Fapp.
Ans: {3.33 J}
b. The mechanical energy lost to heat due to friction.
Ans: {.542 J}
c. The energy stored in the spring.
Ans: {.958J}
d. The total mechanical energy of the block and spring.
Ans: {2.79 J}
e. The speed of the moving block.
Ans: {1.47 m/s}
(C) Determine the maximum distance that the spring will have stretched when the block momentarily comes to rest . Ans: {21.5 cm}
BONUS
(D) Determine the maximum speed that the block will attain. Hint: KE is maximum when v is maximum, and KE (as a function of x) is maximum when the derivative of KE with respect to x equals zero. Alternately, observe that v will begin to decrease the moment that the block's acceleration becomes negative.
Ans: {1.54 m/s}

HOMEWORK for CHAPTER 8
Assignment #21 Sections 8-4 & 8-6 Date Due: Fri. Feb. 21
21. A 950 kg VW is moving at 98.0 km/hr {110 km/hr}.
(A) At what speed will a 5250 kg truck have the same momentum as the VW ?
Ans: { vtruck = 5.53 m/s}
(B) At what speed will a 15.0 gram bullet have the same momentum as the VW ?
Ans: { vbullet =1.94x106m/s }
(C) What impulse would the VW exert on a brick wall if the VW collided with the brick wall, coming to a dead stop in .150 seconds ?
Ans: { Jvw = 2.90x104 N-s}
(D) What average force does the wall exerted on the VW (or the VW exert on the wall) during the collision in part C ?
Ans: { Fav = 1.94x105N}
(E) What impulse would the bullet in part B exerts on a brick wall if it embeds itself in the wall, coming to a dead stop in 24.0 milliseconds ?
(F) What average force does the wall exert on the bullet during the time of impact? (Note that the forces is not constant during the collision so equations like F = m a with a = .5 a t2 is not valid during the collision, i.e. you shold not use Newtons second law methods to solve this problem.)
Ans: {Fav = 1.21x106 N}

Assignment #22 Section 8-6 Date Due: Mon. Feb. 24

22. A 5.70 kg {3.80 kg} sphere A collides with a 4.20 kg sphere B. Both spheres are resting on a horizontal, frictionless surface. Sphere A is moving with a speed of 144 cm/s {12.6 m/s} at an angle of 34.80 East of due North. Sphere B is moving to the West at 26.0 cm/s. After the collision the two objects go off at a right angle relative to each other; the sphere A heading due North. (Vector form of the Conservation of momentum.)
(A) What is magnitude and direction of the total momentum of the two spheres before they collide ? Ans: {47.3 N_s, 56.30 N of E}

(B) What is the momentum of sphere A and its velocity after the collision ?
Ans: {39.3 N-s, 10.3 m/s}

(C) What is the momentum of sphere B and its velocity after the collision ?
Ans: {26.2 N-s, 6.24 m/s}

(D) Sketch the momentum vectors before and after the collision; and visually show that the vector sum of the momentum's after collision is equal to the total momentum before the collision.

(E) Determine if the collision is inelastic, perfectly elastic, or hyper-elastic by calculating the energy gained or lost during the collision?
Ans: {E loss = 18.5 J, inelastic}

Assignment #23 Section 8-6 Date Due: Tue. Feb. 25
23. A 5.50 g bullet traveling at 350 m/s {425 m/s} is fired into a 150 g {280 g} block that is moving at 3.30 m/s on a frictionless table top in the same direction as the bullet. The bullet embeds itself 7.60 cm in the block during its impact.

(A) What is the total momentum of the bullet and the block just after the bullet embeds itself in the block ?
Ans: {p after = 3.26 N-s}

(B) What is the final velocity of the bullet and the block ?
Ans: {v f = 11.4 m/s}

(C) How many joules of mechanical energy are converted into heat during the collision?
Ans: {E Heat = 480 J}

(D) What average force does the bullet exert on the block during the collision ?
Ans: {F av = 6,310 N}

(E) How long did it take the bullet to embed itself into the block ?
Ans: {t = 360 ms}
will place Assignment #23 (along with any old assignments you have not picked up) outside my office by Tuesday afternoon.

Few people are capable of expressing with equanimity, opinions which differ from the prejudice of their social environment.
ALBERT EINSTEIN

Assignment #24 Section 8-7 Skip this one - Not Required this quarter
24. A 4.30 kg block A is moving to the right at a speed of +13.0 m/s on a frictionless surface. A 1.80 kg block B is moving to the left with a speed -5.60 m/s {to the right with a speed of +5.60 m/s}. The blocks collide, stick, and move off together.
(A) Determine the velocity of the center of mass of the two blocks before they collide with each other.
Ans: {10.8 m/s}
(B) In the center of mass frame, determine the velocity of the two blocks before and after they collide.
Ans: { uA = +2.18 m/s, uB = -5.21 m/s, uA' = uB' = 0}
(C) What is the initial kinetic energy of the two blocks in both the lab frame and the center of mass frame ?
Ans: { KEo,lab = 392 J, KEo,cm = 34.7 J}
(D) What is the final kinetic energy of the two blocks in both the lab frame and the center of mass frame. How much energy is lost during the collision. Why is the energy lost equal to the initial kinetic energy of the two blocks in the center of mass frame ?
Ans: { KEf,lab = 357 J, KEf,cm = 0, KEloss = 34.7 J}
(E) Determine the kinetic energy of a fictitious particle traveling at the speed of center of mass that has a mass equal to the total mass of the system. Why is this equal to the final kinetic energy of the two blocks after they collide in the lab frame.
Ans: { KEcm = 357 J}

Exam # 3 Wednesday February 26
Chapters 7, & 8

Kinetic Energy & Potential Energy
The Conservation of Energy
Mechanical Energy Loss & Non-conservative Forces
Momentum & Impulse
Conservation of Momentum
Elastic & Inelastic Collisions
Center of Mass Frame
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THOMAS ALVA EDISON