PHYS 261 Lecture Notes - Lecture 3: Inelastic Collision, Radian, Small-Angle Approximation
23 Sep 2018
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PHYS 261 Pre-Lab Solutions
Lab
Question
Answer
1
1. $A$5 means?
Fixed cell
2. How to plot cartesian coordinates
Scatter chart
3. Solver
Minimizes or maximizes a cell by varying
other cells
4. To use a macro, you may have to
first:
Go to view tab and click on the macro
button
5. To exit a lab template:
Enter name and section number and save
file using macro
2
1. You measure the length of the same
side of a block five times and find:
b=11.0, 11.1, 11.2, 11.2, and 11.3
mm. What is the best estimate for b?
11.16 mm
Take the average
2. You measure the length of the same
side of a block five times and each
measurement has an uncertainty of
0.10 mm. What is the uncertainty in
the best estimate for b?
0.0447
=0.10/sqrt(5)
3. You measure the lengths of three
sides of a block and find a=12.23
mm, b=14.51 mm, c=7.45 mm with
an error of ±0.030 mm in each
measurement. What is the
uncertainty in the volume of the
block?
6.8 mm^3
(∆V/V)2=(∆a/a)2+(∆b/b)2+(∆c/c)2
4. A block is measured to have mass
M=25.3 g and volume V=9.16 cm3
with an uncertainty of ∆M=0.050 g in
the mass and ∆V=0.050 cm3 in the
volume. What is the uncertainty in
the density?
0.016 g/cm3
(∆ρ/ρ)2=(∆M/M)2+(∆V/V)2
5. A block is measured to have a
density ρ=2.76 g/cm3 with an
uncertainty of ∆ρ=0.030 g/cm3. Find
chi-squared when the measured
density is compared to the accepted
density ρ =2.70 g/cm3.
χ2=4
χ2=sum((xi-xtheory)/∆xi)2
1. In this lab, the position of a cart will
be measured using a sonic ranger.
This measures the position by:
Emitting an ultrasonic pulse
3
2. A cart of mass m=0.20 kg rides on an
air track that is tilted at an angle 2
degrees from the horizontal. What is
the magnitude of the total force on
the cart?
0.068 N
Mass*9.8*sin θ
3. A cart of mass m=0.25 kg rides on an
air track that is tilted 3 degrees from
the horizontal. What is the
magnitude of the cart's acceleration?
0.51 m/s2
9.8*sin θ
4. A sonic ranger measures positions
X=0.10 m, 0.15 m, 0.22 m, 0.28 m at
times t=0 s, 0.10 s, 0.20 s, and 0.30 s.
Find the magnitude of the average
velocity between t=0.10 s and 0.20 s.
0.7 m/s
∆x/∆t
5. Suppose you measure g=9.7 m/s2
with an uncertainty of ∆g=0.060
m/s2. Is this consistent with the
accepted value g=9.801 m/s2?
Yes
χ2=sum((xi-xtheory)/∆x)2
Chidist(2.83,1)=0.09
USE EXCEL FOR CHIDIST
4
1. Two carts approach each other,
collide, and stick together after the
collision. This is an example of what
type of collision:
Perfectly inelastic collision
2. Two carts collide, and bounce off
each other. If there are no external
forces acting on the system:
The total kinetic energy can change during
the collision, but the total momentum of
the carts must be the same before and
after the collision.
3. A cart with mass 0.30 kg and velocity
0.20 m/s collided on an air-track with
a cart with mass 0.40 kg and velocity
-0.10 m/s. What is the final velocity
in m/s of the two carts if they stick
together?
0.029 m/s
m1v1+m2v2=(m1+m2)vf
5
6
7
8
9
10
11
What provides the vertical force to balance the force of gravity on the pendulum bob?
Tension in the string
What is the maximum height y that the pendulum can reach in this experiment? y0+L
(From surface to the bottom of the pendulum plus the length of the pendulum
Find the theoretical value for the rotation period for a pendulum bob with height y=0.070 m,
length L=0.20 m, y0=0.020 m, and extension arm length r0=0.020 m. Use g=9.801 m/s2. 0.834 s
Period (tau)=2*pi*sqrt((r*sqrt(L^2-(r-r0)^2))/(g*(r-r0)))
r=r0+L*sin(theta)
One radian is equal to how many degrees? 57.3 degrees
(180/pi)
The small angle approximation says that sin(theta)=theta
Document Summary
What is the best estimate for b: you measure the length of the same side of a block five times and each measurement has an uncertainty of. What is the uncertainty in the best estimate for b: you measure the lengths of three sides of a block and find a=12. 23 mm, b=14. 51 mm, c=7. 45 mm with an error of 0. 030 mm in each measurement. What is the uncertainty in the volume of the block: a block is measured to have mass. M=25. 3 g and volume v=9. 16 cm3 with an uncertainty of m=0. 050 g in the mass and v=0. 050 cm3 in the volume. What is the uncertainty in the density: a block is measured to have a density =2. 76 g/cm3 with an uncertainty of =0. 030 g/cm3. Find chi-squared when the measured density is compared to the accepted density =2. 70 g/cm3. Minimizes or maximizes a cell by varying other cells. Go to view tab and click on the macro button.
