PHYS 101 Final Fall 18 Sample Solved PDF

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SAMPLE FINAL FOR PHYS 101...

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PHYS-101

Fall-2018

FINAL

14 December 2018

NAME__________________________________ Favorite Color___________ Notes: 1. For problems 3 - 6 you should show your work and the answers must contain appropriate units to get full credit. 2. Please read the problems carefully. Relax, and good luck.

g = 9.8 m/s2 ≈ 10 m/s2 x − x0 = v

0xt

2

+ 1/2a xt

dv x dt

2 v2x = v0x + 2ax (x− x0 )

arad = ω 2 r

atan = r α →

→

→

∑ F = F N et = ma→

ax =

dx dt

v x = v 0x + a xt

arad = v 2/r

v = rω →

vx =

ωz =

dθ dt

αz =

f s < f s.max = μsn

F a→b = − F b→a

dωz dt

f k = μk n

F Spring = − kx P2

∫

ΔW 1→2 =

→

→

F • dl

W T ot = K 2 − K 1 = ΔK

F x =−

P1

K = 1/2mv 2

U = mgh

p→ = mv→

∑F =

→

E elastic = 12kx2

→

dp dt

θ = θ0 + ω 0 t + 1/2αt 2 →

I = Σi mi r2i

→

J =

K rot = 1/2Iω 2

I Sphere = 2/5mR2 I Ring = mR2 →

K = 1/2mv 2cm + 1/2I cmω 2

→

∑ →τ =

→

→

→ L = Iω

∆W ∆t

→

= F • →v

2 ω2z = ω0z + 2αz (θ − θ0 )

τ = r→ × F

∑ →τ = τ→N et = I α→

P =

p→2 − p→1

ω z = ω0z + αz t

I Disk = 1/2mR2

→ L = r→ × p→ = →r × mv

→

∫ F dt =

dU (x) dx

I Rod,cm = 1/12mL 2 ΔW 1→2 =

θ2

∫

θ1

τ z dθ

→

dL dt

Student ID _____________ 1

Problem 1. Please circle the answer of your choice for each part [I] through [IV].  Each part is worth 5 pts.

 ith M > m) slide with the same [I] Two objects, both made of the same material, (m  and M, w initial velocity across a table. The coefficient of kinetic friction is 𝜇k = 0.4. Which object slides further before coming to rest? [a] the smaller mass m   slides further than the larger mass M . [b] the larger mass M   slides further than the smaller mass m . [c] each mass will slide the same distance. [d] impossible to tell.

 ith M > m) have the same linear momentum. Which of the [II] Two masses (m   and M, w following is true? [a] the kinetic energy of m   is smaller than the kinetic energy of M . [b] the kinetic energy of M  is smaller than the kinetic energy of m . [c] the kinetic energy of M   is equal to the kinetic energy of m .

[III] A ball of putty and a rubber ball of equal mass are dropped simultaneously from the same height h. The putty sticks to the floor while the rubber ball bounces back to a height equal to 0.75h. [a] The impulse received from the floor on the putty is greater than from the floor on the rubber ball. [b] The impulse received from the floor on the rubber ball is greater than from the floor on the putty. [c] The impulse received from the floor is the same for both the rubber ball and the putty.

[IV] A ring and a solid disc of the same mass M and radius R  are rolling without slipping on a horizontal floor. They are moving with the same translational speed when they encounter an incline. The disc and the ring continue rolling up the incline without slipping. Which one will travel farther up the incline? [a] The disc [b] The ring [c] Both will travel the same distance.

Student ID _____________ 2

Problem 2. (30 points) Short Answers, each part is worth 10 points. [I]. (10 points) My dog was sitting and runs across the yard to bark at a motorcycle. Make a velocity vs time graph for the dog as it runs across the yard.

[II]. (10 points) A bicycle rider is at rest, accelerates for a while, then moves at constant velocity before slowing to a stop at a stop sign. Make energy bar charts or energy pie charts for this process.

[III]. (10 points) A clothes dryer spins a shirt in a horizontal circle at 120 revolutions per minute, the shirt sticks to the wall of the dryer. Make a force diagram for the shirt.

Student ID _____________ 3

Problem 3 (30 points). A block (mass = 4 kg) is placed against the vertical front of a cart as shown in the figure to the right.

[a] (10 pts.) Make Force Diagrams for the block.

[b] (15 pts.) What acceleration must the cart have so that block A  does not fall? The coefficient of static friction between the block and the cart is μ s  = 0.8. Start by using Newton’s 2nd Law: ΣF x = F N = ma ΣF y = F g − F f = 0 ⇒ F g = F f = μsf F N then, solving for FN, F N =

Fg μsf

=

4kg *10m/s2 0.8

= 50N

from there, you can find the acceleration a =

50N 4kg

= 12.5 m/s 2

[c] (5 pts.) What would happen if the cart accelerated slower than the value you calculated in part b? If the cart accelerated more slowly, the normal force would be smaller, making the frictional force smaller. If the frictional force became smaller, then the gravitational force would be bigger than the frictional force. There would be a net force downward force and the block would slide down.

Student ID _____________ 4

Problem 4 (30 points) Dario, a prep cook at an Italian restaurant, spins a salad spinner and observes that it rotates 20.0 times in 5.00 seconds and then stops spinning it. The salad spinner rotates 6.00 more times before it comes to rest. Assume that the spinner slows down with constant angular acceleration. [a] (10 pts.) What is the angular displacement (in radians) of the salad spinner as it slows down? The angular displacement is θ = 6 rev = 12π rad

[b] (10 pts.) What is the angular acceleration of the salad spinner as it slows down? The initial angular velocity is ω = 205 rev = 40π5 rad = 8π rad/s , then we can find the angular s s 2 2 2 acceleration using ω f = ω0 + 2αΔθ then, 0 = (8π rad/s) + 2α(12π rad) then α =

2

−64π2 rad /s2 24π rad

=− 2.67πrad/s2 =− 8.4 rad/s2

[c] (10 pts.) How long does it take for the salad spinner to come to rest? To find the time, use ω f = ω 0 + αt then 0 = 8π rad/s − 2.67πrad/s2 * t solving for t t =

8π rad/s 2.67π rad/s2

= 3s

Student ID _____________ 5

Prob. 5 (30 pts.) J ennifer has a mass of 60.0 kg is standing on top of a chair (1.1 m) to replace a lightbulb. Her sister bumps the chair and knocks Jennifer off the chair. [a] (10 pts.) Make Energy Bar Charts or Energy Pie Charts for Jennifer?

[b] (10 pts.) What was Jennifer’s kinetic energy when she is at a height of 0.45 m above the ground?

[c] (10 pts.) What is the velocity of Jennifer when she hits the ground?

Student ID _____________ 6

Prob. 6 (30  pts) A large vampire bat (0.035 kg) is flying horizontally at 20 m/s when it eats a bug (0.005 kg) that is hovering in the path of the bat. [a] What is the speed of the bat after eating the bug? This is a momentum problem, the momentum of the bat and bug before and after the bat eats the bug must be equal. pbat + pbug = pbad+bug ⇒ 0.035kg * 20m/s + 0 = 0.04kg * vbat+bug 0.7kgm/s = 0.04kg * v v=

0.7 kgm/s 0.04kg

= 17.5 m/s

[b] What impulse did the bug give the bat? Impulse is the chage of momentum. So, the Δp = pfinal − pinit = 0.035kg * 17.5m/s − 0.035kg * 20m/s =− 0.0875kg * m/s

[c] Show that the collision is an inelastic collision. In an inelastic collision the final kinetic energy is less than the initial, so check the initial and final kinetic energy. E k−init = 21 (0.035kg)(20 m/s) 2 = 7J E k−final = 12 (0.04kg)(17.5 m/s)2 = 6.125 J So since the final is less than the intitial it must be an inelastic collision

Student ID _____________ 7

Extra Credit Problem (15 pts.) A solid disk of radius (R = 0.1m) and mass (M = 0.2 kg) rolls down an incline without slipping as shown. What is the speed of the disk when it reaches the bottom of the incline? (Use g = 10 m/s2)

Student ID _____________ 8

You can use this blank page if you need more space.

Student ID _____________ 9...