# 10.2: Unit 10 Practice and Assessment

- Page ID
- 17791

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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)## Outcome 1

1) A rubber ball is lifted to a height of 3.0 **m** at constant speed and then dropped. The ball bounces off the floor below and returns to a height of 2.2 **m**.

a) Does the ball have the same mechanical energy after the bounce as before? If not, where did that mechanical energy go?

2) Fill in the blanks in the following statements about the ball in question 1) using the terms listed. Don’t forget that the body is not 100% efficient.

- chemical potential
- gravitational potential
- elastic potential
- kinetic
- thermal
- positive
- negative
- zero

a) While lifting the ball up, ____________________energy is being exchanged for _________________ energy. The exchange occurs as you do __________work and gravity does __________ work. The ball moves at constant speed because the net work is ________.

b) While falling, gravity is the only force doing work and that work is _____________, therefore the net work is __________ and __________energy is increasing. Overall, ____________________energy is being exchanged for _________________ energy.

c) While in contact with the floor and compressing, the normal force from the floor is doing _________ work, gravity is doing_____________ work. The ball is slowing down so net work must be ___________. Therefore the normal force must be larger than the weight of the ball. Overall, __________________energy and a bit of gravitational potential energy are being exchanged for _______________ energy and ______________energy. (Remembering that the ball does not reach the same height after bouncing).

d) While in contact with the floor and decompressing, the normal force from the floor is doing _________ work, gravity is doing_____________ work. The ball is speeding up so net work must be ___________. Therefore the normal force must be larger than the weight of the ball. Overall, __________________energy is being exchanged for _______________ energy ___________energy and a bit of gravitational potential energy.

e) While rising, gravity is the only force doing work and that work is _____________, therefore the net work is __________ and __________energy is decreasing. Overall, ____________________energy is being exchanged for _________________ energy.

f) Where did the energy come from to do the original work of lifting the ball to increase gravitational potential energy?

## Outcome 2

3) In the absence of gravity or friction, a spaceship engine supplies 55,000 **N** of thrust force to a 1500 **kg** ship.

a) Use the work-energy principle to determine what distance the rocket will cover before it reaches a speed of 1200 **m/s** , starting from rest.

b) Use the impulse-momentum theorem (discussed in the previous unit) to determine how long it will take the rocket to get up to 1200 **m/s** speed. (This is also how long it took to cover that distance you found above).

4) A car is moving at 55 **mph **(26 **m/s**)on flat ground when a hazard is spotted 85 **m **(278 **ft**) ahead. (Such as deer, tree-limb, or broke-down car in the road).

a) What distance does the car travel before the brakes are even applied if the driver takes typical 1.5 **s **braking reaction time? ^{[1]}

b) Draw a free body diagram of this car, while brakes are applied.

c) What is the normal force on the car?

d) If the car slams on the brakes what is the frictional force? Assume that the car has anti-lock bakes that prevent sliding and the static friction coefficient between tire rubber and dry asphalt is 0.7.

e) Use the work-energy principle to determine the stopping distance.

f) What is the total stopping distance including distance covered during the reaction time and braking? Does an accident occur?

## Outcome 3

5) A person uses a pulley system with mechanical advantage of three to lift a 65 **kg** load a distance of 0.5 **m. **

a) What force should the person need to apply?

b) What distance do they need to pull the rope? [Hint: Assuming friction in the pulleys is small enough to ignore, the work input to the pulley system and work output need to be the same].

b) How much potential energy is gained by the load?

c) If the person actually had to pull with 701 **N** due to friction in the system, how much work did they actually do?

d) What is the mechanical efficiency of this system?

e) Remembering that the body is only 20% mechanically efficient, how much chemical potential energy did the person expend?

6) Recently Colin Haley set a speed record for ascending the classically difficult Cassin Ridge on Denali, the highest mountain in North America, located in Central Alaska. Haley started from the glacier at the foot of the mountain and climbed 8000 **ft** to reach the 20,310 **ft **summit in 487 minutes. ^{[2]}

a) If Colin plus his clothes, gear, and light pack had a combined weight of 72 **kg**, how much gravitational potential energy did Colin gain (in units of Joules)?

b) If Colin is 15% mechanically efficient climbing ice and slogging through snow, how many Joules of chemical potential energy did he actually expend?

c) How many Joules of chemical potential energy were converted to exhaust heat?

## Outcome 4

d) What was Colin’s average mechanical power output in Watts?

e) What was Colin’s average thermal power output in Watts?

f) What was Colin’s total average power output in Watts?

g) How many 260 Calorie candy bars would Colin need to eat during his climb in order maintain a constant internal energy? [Hint: Remember, Calories are not the same as calories]

7) A typical microwave oven requires 1,100 **W** of electric power. The microwave needs 2.0 minutes to bring 0.25 **kg** of room-temperature water to a boil.

a) How much electrical potential energy does the microwave use in that time?

b) The thermal energy required to raise the temperature of 0.25 **kg **water from room temp to boiling is 84,000 **J** (more on this in the next unit). What is the efficiency of the microwave in converting electrical potential energy to thermal energy in water?