PHY251 Exam 1 Fall 2020 Name: Directions: YOU MUST WORK ALONE. You may reference any course material and use a cal- culator. External references are allowed with an accompanied citation. Please show...

just answer the questions


PHY251 Exam 1 Fall 2020 Name: Directions: YOU MUST WORK ALONE. You may reference any course material and use a cal- culator. External references are allowed with an accompanied citation. Please show all work. Box and clearly label your final answers. Concepts and Short Answer Figure 1: 1. Two projectiles are fired from a Destroyer at the same velocity as in Figure 1. Which Enemy is hit first? (Include an explanation for partial credit.) a) Enemy 1 c) Both at the same time. b) Enemy 2 d) Not enough information to tell. 2. A swimmer orients herself against current ~vW such that she wants to travel directly across the stream to X as in Figure 3. What must be true about her velocity ~vS? (Take the direction of the current as the positive x-direction.) a) |~vS | > |~vW | c) |~vS | ≤ |~vW | b) |~vS | = |~vW | d) under no condition can she reach X. Figure 2: Figure 3: 3. A mass M that sits on a horizontal frictionless table as shown in Figure 2. Force ~F1 has a magnitude of F1 acts on the mass and is directed at an angle θ1 from the x direction. The normal force n is a) > mg b) < mg c) = mg d) no way to tell. 4. continuing from 3, the mass in figure 2 is also at rest. the magnitude of the static friction force is a) µsmg b) µs(mg + f1 sin θ) c) f1 cos θ d) f1 5. convert 61.2 kilometers per hour (km/hr) to meters per second m/s. 1 patrick cipriano almeida hw phy251 exam 1 fall 2020 figure 4: 6. figure 4 shows a graph of velocity versus time. the displacement, ∆x=x2 − x1, from t1=0 s to t2=1.0 s is a) 3.0 m b) 1.5 m c) 0.0 m d) no way to tell. 7. a car driver travelling a constant 17 m/s takes a turn with an effective radius of 200 m. calculate the acceleration of the car and indicate the direction the acceleration points? 8. a particle’s velocity is described by the equation v(t) = 3.0− 9.9t2 where x(t = 0) = x0 = 0 m. (the numbers in v(t) represent t is seconds and v(t) in m/s). a. find a(t). b. find a(t) when t=1 s. c. find x(t). 2 phy251 exam 1 fall 2020 question i. two vectors, ~a = 3̂i and ~b = 3̂i+ 4ĵ, are defined in the x-y plane. a. draw ~b − ~a. b. calculate the magnitude and direction of ~b − ~a. c. calculate ~a · ~b. d. calculate the angle between ~a and ~b. e. use the right hand rule to indicate the direction of ~a× ~b. extra credit. calculate ~a× ~b. 3 phy251 exam 1 fall 2020 figure 5: question ii. an airplane flying at v0=42.5 m/s parallel to the ground drops supplies to hikers as in figure 5. it takes t=2.47 s for the supplies to hit the ground. a. calculate the initial x- and y-components of velocity, v0x and v0y, just after the supplies leave the plane. b. calculate the distance h as drawn. c. calculate the distance d as drawn. d. fill in the graphs below as they relate to this problem. figure 6: extra credit calculate the magnitude and direction of the velocity just before it hits the ground. 4 phy251 exam 1 fall 2020 figure 7: question iii. a mass m=10.0 kg is connected to a massless rope on an frictionaless inline defined by angle θ=45◦ as in figure 7. a. someone holds the mass at rest. calculate the tension ta in the rope. b. someone eases the mass down the ramp at a constant speed. calculate the tension tb in the rope. c. the mass is now pulled back up the ramp with an acceleration of 1 m/s2. calculate the tension tc in the rope. d. now assume there is kinetic friction on the ramp with coefficient µk=0.1. the mass is allowed to slide down the ramp without a rope attached. calculate the acceleration of the mass. e. how would the inclusion of kinetic friction on the ramp affect your answer to b? would it (a) increase the tension, (b) decrease the tension, or (c) leave the tension unchanged? extra credit. revisit parts b and/or c assuming there is kinetic friction with coefficient of kinetic friction µk=0.1 and calculate the tension. 5 phy251 exam 1 fall 2020 figure 8: question iv. a hanging block m2= 9.0 kg is connected by a massless pulley to block m1=m2/3=3.0 kg as in figure 8. calculate the acceleration of the system. you must include free-body diagram(s) and show your derivation for full credit. 6 mg="" c)="mg" d)="" no="" way="" to="" tell.="" 4.="" continuing="" from="" 3,="" the="" mass="" in="" figure="" 2="" is="" also="" at="" rest.="" the="" magnitude="" of="" the="" static="" friction="" force="" is="" a)="" µsmg="" b)="" µs(mg="" +="" f1="" sin="" θ)="" c)="" f1="" cos="" θ="" d)="" f1="" 5.="" convert="" 61.2="" kilometers="" per="" hour="" (km/hr)="" to="" meters="" per="" second="" m/s.="" 1="" patrick="" cipriano="" almeida="" hw="" phy251="" exam="" 1="" fall="" 2020="" figure="" 4:="" 6.="" figure="" 4="" shows="" a="" graph="" of="" velocity="" versus="" time.="" the="" displacement,="" ∆x="x2" −="" x1,="" from="" t1="0" s="" to="" t2="1.0" s="" is="" a)="" 3.0="" m="" b)="" 1.5="" m="" c)="" 0.0="" m="" d)="" no="" way="" to="" tell.="" 7.="" a="" car="" driver="" travelling="" a="" constant="" 17="" m/s="" takes="" a="" turn="" with="" an="" effective="" radius="" of="" 200="" m.="" calculate="" the="" acceleration="" of="" the="" car="" and="" indicate="" the="" direction="" the="" acceleration="" points?="" 8.="" a="" particle’s="" velocity="" is="" described="" by="" the="" equation="" v(t)="3.0−" 9.9t2="" where="" x(t="0)" =="" x0="0" m.="" (the="" numbers="" in="" v(t)="" represent="" t="" is="" seconds="" and="" v(t)="" in="" m/s).="" a.="" find="" a(t).="" b.="" find="" a(t)="" when="" t="1" s.="" c.="" find="" x(t).="" 2="" phy251="" exam="" 1="" fall="" 2020="" question="" i.="" two="" vectors,="" ~a="3̂i" and="" ~b="3̂i+" 4ĵ,="" are="" defined="" in="" the="" x-y="" plane.="" a.="" draw="" ~b="" −="" ~a.="" b.="" calculate="" the="" magnitude="" and="" direction="" of="" ~b="" −="" ~a.="" c.="" calculate="" ~a="" ·="" ~b.="" d.="" calculate="" the="" angle="" between="" ~a="" and="" ~b.="" e.="" use="" the="" right="" hand="" rule="" to="" indicate="" the="" direction="" of="" ~a×="" ~b.="" extra="" credit.="" calculate="" ~a×="" ~b.="" 3="" phy251="" exam="" 1="" fall="" 2020="" figure="" 5:="" question="" ii.="" an="" airplane="" flying="" at="" v0="42.5" m/s="" parallel="" to="" the="" ground="" drops="" supplies="" to="" hikers="" as="" in="" figure="" 5.="" it="" takes="" t="2.47" s="" for="" the="" supplies="" to="" hit="" the="" ground.="" a.="" calculate="" the="" initial="" x-="" and="" y-components="" of="" velocity,="" v0x="" and="" v0y,="" just="" after="" the="" supplies="" leave="" the="" plane.="" b.="" calculate="" the="" distance="" h="" as="" drawn.="" c.="" calculate="" the="" distance="" d="" as="" drawn.="" d.="" fill="" in="" the="" graphs="" below="" as="" they="" relate="" to="" this="" problem.="" figure="" 6:="" extra="" credit="" calculate="" the="" magnitude="" and="" direction="" of="" the="" velocity="" just="" before="" it="" hits="" the="" ground.="" 4="" phy251="" exam="" 1="" fall="" 2020="" figure="" 7:="" question="" iii.="" a="" mass="" m="10.0" kg="" is="" connected="" to="" a="" massless="" rope="" on="" an="" frictionaless="" inline="" defined="" by="" angle="" θ="45◦" as="" in="" figure="" 7.="" a.="" someone="" holds="" the="" mass="" at="" rest.="" calculate="" the="" tension="" ta="" in="" the="" rope.="" b.="" someone="" eases="" the="" mass="" down="" the="" ramp="" at="" a="" constant="" speed.="" calculate="" the="" tension="" tb="" in="" the="" rope.="" c.="" the="" mass="" is="" now="" pulled="" back="" up="" the="" ramp="" with="" an="" acceleration="" of="" 1="" m/s2.="" calculate="" the="" tension="" tc="" in="" the="" rope.="" d.="" now="" assume="" there="" is="" kinetic="" friction="" on="" the="" ramp="" with="" coefficient="" µk="0.1." the="" mass="" is="" allowed="" to="" slide="" down="" the="" ramp="" without="" a="" rope="" attached.="" calculate="" the="" acceleration="" of="" the="" mass.="" e.="" how="" would="" the="" inclusion="" of="" kinetic="" friction="" on="" the="" ramp="" affect="" your="" answer="" to="" b?="" would="" it="" (a)="" increase="" the="" tension,="" (b)="" decrease="" the="" tension,="" or="" (c)="" leave="" the="" tension="" unchanged?="" extra="" credit.="" revisit="" parts="" b="" and/or="" c="" assuming="" there="" is="" kinetic="" friction="" with="" coefficient="" of="" kinetic="" friction="" µk="0.1" and="" calculate="" the="" tension.="" 5="" phy251="" exam="" 1="" fall="" 2020="" figure="" 8:="" question="" iv.="" a="" hanging="" block="" m2="9.0" kg="" is="" connected="" by="" a="" massless="" pulley="" to="" block="" m1="m2/3=3.0" kg="" as="" in="" figure="" 8.="" calculate="" the="" acceleration="" of="" the="" system.="" you="" must="" include="" free-body="" diagram(s)="" and="" show="" your="" derivation="" for="" full="" credit.="">