PHY-251 Exam 2 Spring 2020
Name:
Directions: Please show all work. Box and clearly label your final answers. Calculators and one
handwritten page of notes are allowed. No talking, phones, or computers.
Concepts and Short Answe
1. A rope pulls a mass M up an incline from a height of 0 m to a height H at a constant speed as in
Figure 1. The work done by the tension WT =
a) MgH b) −MgH sin θ c) −MgH d) 0
2. The NET work on M being up an incline from a height of 0 m to a height H at a constant speed
(as in Figure 1) is =
a) MgH b) −MgH sin θ c) −MgH d) 0
Figure 1: Figure 2:
3. A block with mass m travels with velocity v toward a spring with spring constant k on a frictionless
surface as in Figure 2. The spring is compressed distance xm = from equili
ium x = 0.
a)
√
m
k v c)
kv
m
)
√
k
mv d) Not enough information.
4. A skater of mass m travels to a wall in the negative x direction with velocity v, bounces off of the
wall, then travels in the positive x direction with the same velocity v as in Figure 3. The magnitude of the
change in momentum is
a) 0 b) 2mv c) mv2 d) mv
Figure 3: Figure 4:
5. The force F as a function of position x is shown in Figure 4. The work W done between x1=4.0 m
and x2=6.0 m
a) 20 J c) 80 J
) 40 J d) 10 J
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Patrick Cipriano Almeida
Patrick Cipriano Almeida
PHY-251 Exam 2 Spring 2020
Figure 5: Figure 6:
Question 1. Initially mass m1=1.0 kg moves with velocity v1i=4.0 m/s in the positive x-direction
toward mass m2=5.0 kg that is also moving at v2i=1.0 m/s positive x-direction as in Figure 5. After the
masses collide m2 continues moving to the right at v2f=2.0 m/s.
A. Calculate the final velocity of m1, vf1. Indicate the direction.
B. Determine if the collision is elastic or inelastic. Show quantitatively.
Question 2. Suppose F = t2 − t5 represents a force the acts on the interval ti=0 s and tf=1 s as in
Figure 6.
A. Calculate the impulse associated with this force on the interval ti=0 s and tf=1 s?
B. Calculate the average force Fave on the interval ti=0 s and tf=1 s?
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PHY-251 Exam 2 Spring 2020
Figure 7:
Question 3. An asteroid of mass m=8.7×1016 kg falls to Earth (ME=5.98×1024 kg, RE=6.4×106 m)
from a height h=7RE above the Earth as in Figure 7. The gravitational constant G=6.67×10−11 N m2/kg2.
A. Calculate the force of gravity FG between the Earth and the asteroid at height h above the surface
of the Earth (assume the size of the asteroid is negligible to the size of the Earth).
B. If the initial velocity of the asteroid is approximately zero vi=0, calculate final velocity vf does the
asteroid have when it lands on the surface of Earth.
Question 4. Work
A. A force F=6x5 acts between x0=0 and x=2. Calculate the work W done on this interval?
B. A constant force ~F=3̂i + 1ĵ acts between ~r0=0̂i + 0ĵ and ~r=1̂i + 3ĵ. What is the work W done on
this interval?
C. A potential energy is described as U=-xy2. Find the x- and y-components of the force, Fx and Fy
espectively.
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PHY-251 Exam 2 Spring 2020
Question 4. A soccer ball of mass msb=0.43 kg kicked due west at velocity vsb,i=27.0 m/s during a
practice collides with a rock mr=0.3 kg that is initially at rest. Just after the collision, the soccer ball is
moving at vsb,f=9.0 m/s at θsb,f=20
◦ south of east.
A. Draw a picture of the system.
B. Use conservation of momentum in the y- direction to calculate the y-component of the momentum of
the rock py,r,f after the collision.
C. Use conservation of momentum in the x- direction to calculate the x-component of the momentum of
the rock px,r,f after the collision.
D. Calculate the magnitude pr,f and direction θr,f of the rock after the collision.
EXTRA CREDIT Is the collision elastic or inelastic? Show quantitatively.
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PHY-251 Exam 2 Spring 2020
Figure 8:
Question 5. A block of mass m=5.0 kg and velocity v0 travels toward an incline at angle θ=20.0
◦ as
in Figure 8. Just before the mass encounters the incline it experiences a d=1.00 m patch of ground with
friction (µk=0.1), where the rest of the ground and the incline itself are frictionless. Just at the end of this
patch, which is right before the mass goes up the incline, the velocity of the mass is v=25.0 m/s.
A. Calculate the work done by friction Wfriction.
B. Calculate the velocity v0 before the mass experienced friction.
C. Calculate the maximum height Hmax the mass reaches on the incline.
EXTRA CREDIT If the incline had the same coefficient of friction as the patch (µk=0.1), calculate
the new maximum height H ′max the mass reaches on the incline.
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