Two objects are at rest on a frictionless surface. Object 1 has a greater mass than object 2.
(a) When a constant force is applied to object 1, it accelerates through a distance d. The force is removed from object 1 and is applied to object 2. At the moment when object 2 has accelerated through the same distanced, which statements are true? (Select all that apply.)
1. K1 < K2
2. p1 > p2
3. p1 = p2
4. p1 < p2
5. k1 = K2
6. k1 > k2
(b) When a force is applied to object 1, it accelerates for a time interval Δt. The force is removed from object 1 and is applied to object 2. Which statements are true after object 2 has accelerated for the same time interval Δt? (Select all that apply.)
1. K1 > K2
2. p1 < p2
3. k1 < K2
4. k1 = k2
5. p1 > p2
6. p1 = p2
Linear Momentum & Kinetic Energy
To compare the momentum and kinetic energy of two objects, we need to know the mass of the object and the speed acquired by the moving object. To solve this problem, we need to take advantage of the work-energy theorem and the impulse-momentum theorem.
According to the work-energy theorem:
W
net
=
Δ
K
According to the impulse-momentum theorem, we write:
I
m
p
u
l
s
e
=
C
h
a
n
g
e
i
n
m
o
m
e
n
t
u
m
The momentum of the object is calculated by using the following formula:
|
→
p
|
=
m
v
The kinetic energy of the object is calculated by using the following formula:
K
=
1
2
m
v
2
where m
is the mass of the object, v
is the speed of the object, and K
is the kinetic energy of the object.