Physics 8 — Friday, September 6, 2013

I HW1 took most people about 2 hours; if HW1 took you 3-4hours, you should find a couple of classmates with whom youcan discuss the HW. Also come by on Wed/Thu evenings.

I I will put HW2 online later today. Printed copies Monday.

I Read Ch3 (acceleration) for Monday & send online response.

I I read all responses before class (helps me focus on keytopics), and try to respond individually to about 1/3 of them.

I Bill hosts HW study/help sessions on Thursdays at 7pm inDRL 3W2 (started this week).

I Zoey hosts HW study/help sessions on Wednesdays at 7pm inDRL 2N36 (starting next week).

I Free physics tutoring (by physics majors) for intro physicscourses, M–Th 3–7pm in Room 253 of Education Commonsin Weiss Pavillion.

I I marked up Weds. slides with answers & corrections in red.

Is anything unclear from the material covered so far(Chapters 1 & 2)?

On HW1, people singled out

I problem 7 (husband & wife meet for lunch),

I problem 6 (equations for projectile),

I problem 1 (mass of glass curtain wall), and maybe also

I problem 5 (walk to restaurant & back).

An object goes from one point in space to another. After it arrivesat its destination, the magnitude of its displacement is:

(a) either greater than or equal to

(b) always greater than

(c) always equal to

(d) either smaller than or equal to

(e) always smaller than

(f) either smaller or larger than

the total distance traveled by the object.

Slope of the x(t) curve

The slope (also known as derivative, dxdt ) of the curve in a

position (x) vs. time (t) graph for an object’s motion gives

(A) the magnitude of the object’s acceleration

(B) the x component of the object’s acceleration

(C) the magnitude of the object’s average velocity

(D) the x component of the object’s average velocity

(E) the magnitude of the object’s instantaneous velocity

(F) the x component of the object’s instantaneous velocity

(G) the magnitude of the object’s displacement

(H) the x component of the object’s displacement

(I) the object’s speed

Representing motion as x vs. tA person initially at point P in the illustration stays there amoment and then moves along the axis to Q and stays there amoment. She then runs quickly to R, stays there a moment, andthen strolls slowly back to P. Which of the position vs. timegraphs below correctly represents this motion? 2/B

Below I graphed an object’s position (x) vs. time (t). Is the valueof vx (the x component of the object’s velocity) at t = 25 s

(a) smaller than

(b) the same as

(c) larger than

(d) (not enoughinformationgiven)

the value of vx at t = 10 s?

Below I graphed an object’s position (x) vs. time (t). Is the valueof vx (the x component of the object’s velocity) at t = 25 s

(a) smaller than

(b) the same as

(c) larger than

(d) (not enoughinformationgiven)

the value of vx at t = 10 s?

Below I graphed an object’s position (x) vs. time (t). Is theobject’s speed at t = 25 s

(a) smaller than

(b) the same as

(c) larger than

(d) (not enoughinformationgiven)

the object’s speed at t = 10 s?

Similar to #6 and #5 combined.

A mouse runs along a baseboard in your house. The mouse’sposition x as a function of time t is given by

x(t) = qt − pt2

with q = 2.0 m/s and p = 0.50 m/s2.

At what time (or times) does the mouse’s position equal 1.0 m ?

Technically, x is the x component of the mouse’s position vector,but it can be tedious to speak so precisely.

Solving quadraticequation gives twosolutions:t = 0.586 s,t = 3.41 s.

What is the mouse’s distance traveled from t = 0 to t = 4.0 s ?

What is the mouse’s average speed from t = 0 to t = 4.0 s ?

What is mouse’s average velocity vx ,av from t = 0 to t = 4.0 s ?

A mouse runs along a baseboard in your house. The mouse’sposition x as a function of time t is given by

x(t) = qt − pt2

with q = 2.0 m/s and p = 0.50 m/s2.

Calculate and graph (the x component of) the mouse’s velocity vx

from t = 0 to t = 4.0 s.

x(t) = qt − pt2

with q = 2.0 m/s and p = 0.50 m/s2.

Calculate and graph (the x component of) the mouse’s velocity vx

from t = 0 to t = 4.0 s.

vx =dx

dt= q − 2pt = (2.0 m/s)− (1.0 m/s2)t

Modified version of #7.

A husband and wife work in buildings ten blocks apart and plan tomeet for lunch. The husband strolls at 1.0 m/s, while the wifewalks briskly at 1.5 m/s. Knowing this, the wife picks a restaurantbetween the two buildings at which she and her husband will arriveat the same instant, if the two leave their respective buildings atthe same instant. In blocks, how far from the wife’s building is therestaurant?

(If we’re ahead of schedule)

Two runners in a 100 meter race start from the same place.Runner A starts as soon as the starting gun is fired and runs at aconstant speed of 8.00 m/s. Runner B starts 2.00 s later and runsat a constant speed of 9.30 m/s.

(a) Who wins the race?

(b) At the instant she crosses the finish line, how far is the winnerahead of the other runner?

Chapter 3 reading (for Monday): acceleration.

Working in 1 dim. (I’ll write x components instead of vectors),

I position: x

I displacement: xf − xi

I (instantaneous) velocity: vx = dxdt

I average velocity: vx ,av = xf−xitf−ti

I (instantaneous) acceleration: ax = dvxdt = d2x

dt2

I average acceleration: ax ,av =vx,f−vx,i

tf−ti

Velocity is the rate of change of position. Acceleration is the rateof change of velocity. Both are vector quantities.

Objects moving in “freefall” in Earth’s gravitymove with a constantdownward acceleration, ofmagnitude g = 9.8 m/s2.

(“Down” means towardEarth’s center.)

I Objects moving in “free fall” in Earth’s gravity move with aconstant downward acceleration, of magnitude g = 9.8 m/s2.

I “Down” means toward Earth’s center.

I If we define the x axis to point upward, then

ax = −g

I For the (very useful) special case of motion under constantacceleration, we can integrate the above equation to get(R.H.S. is for the case of free-fall motion)

vx(t) = vx ,i + ax t = vxi − gt

I Then we can integrate again to get (R.H.S. = free fall)

x(t) = xi + vx ,i t +1

2ax t

2 = xi + vx ,i t −1

2gt2

I One more useful consequence of ax = constant is

v2x ,f = v2

x ,i + 2ax (xf − xi )

A low-friction cart travelingdown an inclined planethat makes an angle θ withrespect to the horizontalmoves with a constantdownhill acceleration, ofmagnitude g sin θ.

If we define the x axis topoint downhill, then wehave (note plus sign)

ax = +g sin θ

with g = 9.8 m/s2.

Physics 8 — Friday, September 6, 2013

I HW1 took most people about 2 hours; if HW1 took you 3-4hours, you should find a couple of classmates with whom youcan discuss the HW. Also come by on Wed/Thu evenings.

I I will put HW2 online later today. Printed copies Monday.

I Read Ch3 (acceleration) for Monday & send online response.

I I read all responses before class (helps me focus on keytopics), and try to respond individually to about 1/3 of them.

I Bill hosts HW study/help sessions on Thursdays at 7pm inDRL 3W2 (started this week).

I Zoey hosts HW study/help sessions on Wednesdays at 7pm inDRL 2N36 (starting next week).

I Free physics tutoring (by physics majors) for intro physicscourses, M–Th 3–7pm in Room 253 of Education Commonsin Weiss Pavillion.

I I’ll put today’s slides up on Canvas this afternoon.