Download AP Physics – Newton`s Laws Ain`t Over – 7 ans

AP Physics – Newton’s Laws Ain’t Over – 7 ans
1. A ball is kicked at an angle of 38.0° to the horizontal with a speed of 15.8 m/s. How far does it travel?
m
m
m
m
v y = v sin θ = 15.8 sin 38.00 = 9.73
vx = v cos θ = 15.8 cos 38.00 = 12.45
s
s
s
s
m
m
−9.73 − 9.73
vy − vy 0
s
s
=
= 1.986 s
v y = v y 0 + at t =
m
a
−9.8 2
s
x
m
x = vx t = 12.45 (1.986 s ) =
24.7 m
vx =
s
t
2. What is the mass of a 235 N acrobat?
⎛
⎞
⎜
w
kg ⋅ m
1 ⎟
w = mg
m=
= 235
24.0 kg
⎜
⎟ =
g
s 2 ⎜ 9.8 m ⎟
⎜
s 2 ⎟⎠
⎝
3. A 25.6 kg rocket accelerates upward at 105 m/s2. What is the thrust pushing it up?
m⎞
m⎞
⎛
⎛
ma = FT − w FT = ma + w = 2.56 kg ⎜105 2 ⎟ + 2.56 kg ⎜ 9.8 2 ⎟ =
294 N
s ⎠
s ⎠
⎝
⎝
4. When you jump into the air, you push the earth away from you and the earth pushes you away from it.
How come no one notices that you pushed the earth?
5. A 12 250 kg boulder hangs from two cables which are at the angles shown. Calculate the tensions in the
two cables.
23.8
∑ Fy = 0 = T1 sin θ + T2 sin φ − mg = 0
∑ Fx = 0 = T1 cos θ − T2 cos φ T1 = T2
T1 sin θ + T2 sin φ = mg
=
= T2
cos81.80
cos 23.80
( 0.1559 T2 ) sin θ + T2 sin φ = mg
m⎞
⎛
12 250 kg ⎜ 9.8 2 ⎟
s ⎠
⎝
T2 =
0
( 0.1559 ) sin 23.8 + sin 81.80
T1 = 0.1559 T2
cos φ
cos θ
T2 =
=
81.8
0.1559 T2
mg
( 0.1559 ) sin θ + sin φ
T2
T1
θ
=
φ
114 000 N
0.1559 (114 000 N ) =
mg
17 800 N
6. Two masses are connected by a light string which passes over a frictionless
pulley as shown. (a) What is the acceleration of the system? (b) What are the
tensions in the string?
m2 a = T − m2 g
(a) m1a = m1 g − T
T
T
Add ‘em up:
m1a + m2 a = T + m1 g − m2 g − T
m1a + m2 a = m1 g − m2 g
a ( m1 + m2 ) = g ( m1 − m2 )
g ( m1 − m2 )
a=
( m1 + m2 )
m ⎛ 5.25 kg − 5.00 kg
= 9.8 2 ⎜⎜
s ⎝ 5.25 kg + 5.00 kg
⎞
⎟⎟ =
⎠
m
0.239 2
s
5.00 kg
5.25 kg
m2 g
m1 g
m⎞
m⎞
⎛
⎛
T = m1 g − m1a = 5.25 kg ⎜ 9.8 2 ⎟ − 5.25 kg ⎜ 0.239 2 ⎟ =
s ⎠
s ⎠
⎝
⎝
(b) m1a = m1 g − T
7. You pull on a 98.0 kg bag of wild bird seed and drag it across the deck. If the
coefficient of kinetic friction for the bag on the deck is 0.445, what force must you
apply to move the thing at a constant speed?
m⎞
⎛
F = f = μ n = μ mg = 0.445 ( 98.0 kg ) ⎜ 9.8 2 ⎟ =
427 N
s ⎠
⎝
50.2 N
n
f
T
mg
8. Find the acceleration of the system shown in the drawing if the coefficient of kinetic friction between the
7.00 kg mass and the plane is 0.280.
7.00 kg
m1a = T − m2 g sin θ
m2 a = m2 g − T
m1a + m2 a = T − m1 g sin θ + m2 g − T
6.50 kg
m1a + m2 a = m2 g − m1 g sin θ a ( m1 + m2 ) = g ( m2 − m1 sin θ )
35.0
a=g
a=
( m2 − m1 sin θ )
( m1 + m2 )
0.184
= 9.8
m ⎛ 6.50 kg − 7.00 kg sin 35.0
⎜
s 2 ⎜⎝
7.00 kg + 6.50 kg
o
⎞
⎟⎟
⎠
n
m
s2
T
T
f
FX
m2 g
9. A retired policewoman pushes on a 77.2 kg crate with a pole. The
pole makes an angle of 32.0° to the horizontal. The coefficient of
m1 g
kinetic friction for the crate and the deck is 0.350. The
policewoman exerts a force of 535 N. What is the acceleration of the crate?
F cos θ − f
a=
∑ Fx = ma ma = F cosθ − f
m
∑ Fy = 0
n − F sin θ − mg = 0
F
f
n = F sin θ + mg
m⎞
⎛
n = 535 N sin 32.00 + 77.2 kg ⎜ 9.8 2 ⎟ = 1 040 N
s ⎠
⎝
kg ⋅ m
kg ⋅ m ⎞
⎛
535 2 cos 32.00 − 0.350 ⎜1040 2 ⎟
s
s ⎠
89.7 kg
⎝
a=
=
77.2 kg
77.2
n
mg
=
1.16
m
s2
10. Why do all objects fall at the same speed (ignoring air resistance)?
11. The first law says that no force is required to maintain motion. Fine, then how come you have to keep
pedaling your bicycle to keep it moving?
12. What is the difference between mass and weight?
13. Explain, in terms of Newton's laws, the magician's trick of pulling a tablecloth out from under a bunch of
dishes and cups and stuff without disturbing them.
14. What net force is required to accelerate a 135 000 kg aircraft from rest to a speed of 35.0 m/s in 11.0 s?
v = at
a=
v
t
= 35.0
m⎛ 1 ⎞
m
⎜
⎟ = 3.182 2
s ⎝ 11.0 s ⎠
s
m⎞
⎛
F = ma = 135 000 kg ⎜ 3.182 2 ⎟ = 430000 N
s ⎠
⎝
=
4.30 x 105 N
15. A wise guy you know poses this problem to you, "A horse pulls on a cart, exerting a force on it. The cart
exerts an equal and opposite force on the horse. So if the forces are equal, then the net force is zero and
the horse cannot pull the cart." What is wrong about this set of particulars? [I.e., why can the horse pull
the cart?]