Departamento de Engenharia Física da FEUP
Física I / L.EIC - Test, 20-04-2023
DURATION:
1h 00min
LKGAH
COMPLETE NAME (CAPITAL LETTERS):
Smartwatches and smartphone are forbidden.
Electronic calculator is not allowed.
The test has 10 multiple-choice questions. Mark for a correct answer is +2.0, and for wrong answer is -0.4
There is only one correct option. Multiple answers to a given question are not evaluated.
Otherwise indicated, SI units are used.
Consider g =10 ms−2 . Other values: cos 60◦ = sin 30◦ = 1/2; sin 60
1. A stone is thrown vertically up to a maximum
height of 5 m. Assuming there is no air resistance, the initial speed of the stone is:
(a)
(b)
(c)
(d)
(e)
(c)
(d)
(e)
√
= cos 30◦ = 3/2.
3. Consider a mass moving horizontally along the xx
axis, where its accelaration a varies with its speed
v , as a(t) = 2v(t). If the mass is initially at x = 0
with a speed v0 , the equation of its motion x(t)
is given by:
2 m/s.
4 m/s.
6 m/s.
8 m/s.
10 m/s.
(a)
(b)
(c)
(d)
(e)
2. The initial vector velocity of a projectile has an angle of 60◦ above the horizontal. If the initial speed
is 10 m/s, which of the sentences below is true
when the projectile reaches its maximum height?
(a)
(b)
◦
x(t) = v0 t + at2 /2.
x(t) = tv(t).
v0
x(t) = (e2t − 1).
2
x(t) = v0 t(et − 1).
x(t) = v0 t(et − 1)/2.
4. In a 2-D motion, the velocity of a given body is
desribed by ~v (t) = 2tı̂ + 4̂. If the initial position of this body is ~r0 = ı̂, which of the following
expressions relates the horizontal position x with
the vertical one y at a given time t?
The speed is 10 m/s.
The speed is 5 m/s.
√
(a)
(b)
(c)
(d)
(e)
The speed is 5 3 m/s.
The horizontal component of the velocity is zero.
The horizontal component of the velocity is 5 m/s.
1
x = 1 − y2 .
x = 1 + y2 .
x = 1 + y 2 /4.
x = 1 + y 2 /8.
x = 1 + y 2 /16.
2/1
5. A particle with a mass m = 2 Kg, moves without
friction along the xx axis. If the potential energy
of this particle is given by Ep (x) = −3x3 + x4
J, what will be its speed when x = 1 m, if its
mechanical energy is 7 J?
(a)
(b)
(c)
(d)
(e)
0 m/s.
1 m/s.
2 m/s.
3 m/s.
10 m/s.
F⃗2
m
6. A particle, initially at rest, is released from an
incline from a height of 10 cm. Assume there is
no frictional force between the particle and the
surface of the ramp. When the particle reaches
the bottom, it continues to move horizontally during 1 m and then stops. Under these conditions,
what is the coecient of kinetic friction between
the particle and the horizontal surface?
(a)
(b)
(c)
(d)
(e)
8. A heavy block with m = 600 kg, standing on
ice, is pulled by two ropes making an angle of
60◦ (see gure). The magnitude of the constant
force applied to each rope is 1 N. If the block
is initially at rest, what will be its speed after
moving 2 m?
F⃗1
x
(a)
(b)
(c)
(d)
(e)
0.1 m/s.
0.5 m/s.
2 m/s.
10 m/s.
15 m/s.
9. A block with a mass m1 is on an incline (α = 30◦ )
and is attached by a massless string to other block
with a mass m2 (see gure). The fricitional force
between block m1 and the surface is negligible.
What is the relation between the two masses if
the two blocks do not move?
0.9.
0.1.
0.25.
0.
0.7.
7. Consider two blocks (seee gure) with masses m1
and m2 . There is a frictional force only between
block m2 and the horizontal surface, where µe
and µc correspond respectively to the static and
kinetic coecients of friction. When a force F~
is applied to block m1 , the two blocks move together. The accelaration of block 2 is given by:
F~
60◦
m1
m2
(a)
2(µe m1 g+F )
.
3m2
(b)
F −µc m2 g
m1 +m2 .
(c)
F −µc m1 g
.
m2
(d)
F
m2 .
(e)
F
m1 +m2 .
x
m1
m2
α
(a)
(b)
(c)
(d)
(e)
√
m2 = m1 / 2.
m2 = 2m1 .
m2 = m1 /3.
m2 = m1 /4.
m2 = m1 /2.
10. Under the conditions of the previous problem,
consider now that the masses are equal: m1 =m2 .
If block 2 is initially at rest, what would be its
speed after falling down 20 cm?
(a)
(b)
(c)
(d)
(e)
2 m/s.
1 m/s.
0.5 m/s.
0.1 m/s.
0 m/s.
1/1
Answer Key for Exam A
1. (e)
6. (b)
2. (b)
7. (b)
3. (c)
8. (a)
4. (e)
9. (e)
5. (d)
10. (b)