PHYS 103 Fund. of Physics I Unit III Exam, Fall 2021
Summary of Formulas
Momentum: ? = ??
Impulse-momentum theorem: ? = ∆? = ?∆?
Conservation of Total Momentum: total ?? = ????? ??
?1?1 + ?2?2 . . . = ?1?1
′ + ?2?2
′ …
Collisions always conserve momentum
-Elastic collisions also conserve KE
-Inelastic collisions do NOT conserve KE (lose KE)
-Perfectly inelastic collisions lose the most KE (objects stick together after collision)
??????: ? = ? × ? = ?????? (? = ????? ??????? ? ??? ?)
? = ?⊥? = ??(? = ???????????????)
Equili
ium: 1. Rotational Equili
ium, ???? = 0
XXXXXXXXXX2. Translational Equili
ium, ???? = 0
Static Equili
ium means:
???? = ?, ???? = ?, ? = ?
Angular Acceleration: ? =
∆?
∆?
, ??????? ????????: ? =
∆?
∆?
? = ??, ?? = ??
Dynamics of Rotational Motion:
? = ??, ? = ∑ ??2
Rotational Kinetic Energy: ????? =
1
2
??2
Angular Momentum: L = lω
Conservation of Total Angular Momentum: total ?? = total ??
???? = ????
PHYS 103 Fund. of Physics I Unit III Exam, Fall 2021
PHYS XXXXXXXXXXNAME: _________________
UNIT III EXAM
Fall 2021 XXXXXXXXXXSCORE: _________________
Q1. A batter strikes a pitched baseball (mass = 0.2 kg) that was moving horizontally at 30
m/s (to -x direction), and it leaves his bat moving at a speed of 50 m/s directly back (to +x
direction) toward the pitcher. The bat was in contact with the baseball for 10 ms.
a) What’s the baseball’s change in momentum?
) What’s the impulse of the force exerted by the batter?
c) What’s the magnitude of the average force exerted by the bat on the ball? (J=FΔt)
Q2. The graph at the below shows how a force F acting on an object of mass m = 2kg varies
as a function of time.
a) What is the magnitude of the impulse of this force?
) If the object’s initial velocity is +2 m/s, what will be the object’s velocity after this
force acts?
20
10
XXXXXXXXXX
PHYS 103 Fund. of Physics I Unit III Exam, Fall 2021
Q3. Ball 1 and Ball 2 are rolling toward each other at the same speed, 10 m/s. Ball 1 has a mass
of m1 = 8 kg, and Ball 2 has a mass of m2 = 2 kg. After the collision, Ball 1 and Ball 2 stick
together and slide frictionlessly across the table. a) What’s their common velocity after the
collision? b) Was this collision elastic or inelastic? (test whether ??? = ??? ?? ???)
Q4. Two balls are on a frictionless horizontal tabletop. Ball X initially moves at 10 m/s , as
shown in the Figure I above. It then collides elastically with identical ball Y which is initially at
est. After the collision, ball X moves at 6 m/s along a path at 53° to its original direction, as
shown in Figure II above. Find the magnitude and direction of ball Y after the collision.
Q5. A bullet of mass m and velocity vo is fired toward a block of mass 4m. The block is initially at rest
on a frictionless horizontal surface. The bullet penetrates the block and emerges with a velocity of
vo
5
.
(a) Determine the final speed of the block.
(b) Determine the loss in kinetic energy of the bullet.
PHYS 103 Fund. of Physics I Unit III Exam, Fall 2021
Q6. A bullet of mass m is moving horizontally with speed vo (= 5m/s) when it hits a block of mass 10kg
that is at rest on a horizontal frictionless table, as shown above. The surface of the table is a height
h(=1m) above the floor. After the impact, the bullet and the block slide off the table and hit the floor a
distance x from the edge of the table.
(a) Determine the speed of the block as it leaves the table.
(b) Determine the distance x.
Q7. In the figure below, a block of mass 50 kg is held in place by two ropes exerting equal
tension forces. If cos θ = 2/3, what’s the tension in each rope?
Q8. A uniform rigid bar of weight W is supported in a horizontal orientation as shown by a rope
that makes a 30° angle with the horizontal. The force exerted on the bar at point O, where it is
pivoted, is best represented by a vector whose direction is which of the following?
PHYS 103 Fund. of Physics I Unit III Exam, Fall 2021
Q9. A bowling ball of mass M and radius R. whose moment of inertia about its center is
(2/5)MR2, rolls without slipping along a level surface at speed v. The maximum vertical height
to which it can roll if it ascends an incline is
Q10. A particle of mass m moves with a constant speed v along the dashed line y = a. When the
x-coordinate of the particle is xo, the magnitude of the angular momentum of the particle with
espect to the origin of the system is
Q11. A system of two wheels fixed to each other is free to rotate about a frictionless axis through
the common center of the wheels and perpendicular to the page. Four forces are exerted
tangentially to the rims of the wheels, as shown. The magnitude of the net torque on the system
about the axis is
Q12. A light rigid rod with masses attached to its ends is pivoted about a horizontal axis as
shown above. When released from rest in a horizontal orientation, the rod begins to rotate with
an angular acceleration of magnitude.