Download Answer the following questions

Answer the following questions:
1- a) How high can a man throw a ball if he can throw it with initial velocity 8 m/s
(2)
v 2 = vo2 − 2 g ∆ y
0 = (8) − 2(10 ) ∆ y
∆ y = 3.2 m
2
2. A speedboat increases its speed uniformly from 20 m/s to 30 m/s in a time of 5 sec.
(a) Find the magnitude of its acceleration
(2)
v = vo + a t ⇒ 30 = 20 + a (5) ⇒ 30 = 20 + a (5)
a = 2 m / s2
(b) How far does the boat travel during that time?
(2)
 v + vo 
∆x = 
t
 2 
 30 + 20 
∆ x =
 5 =125 m
 20 
B
3- From the figure, find:
70m
a) The x-component of the vector B
(1)
B X = 70 cos120 = − 35 m
b) The y-component of the vector B
(1)
B y = 70 sin 120 = 60.6 m
c) For the vector C= A + B
i)
, find
C X = AX + B X = 20 + (− 35) = − 15 m
(2)
ii)
C y = Ay + B y = 60.6 + 0 = 60.6 m
(2)
iii)
(1)
The direction that C makes with the positive x axis
 60.6 
 + 180 = − 76 + 180 =103.9°
 15 
θ = tan −1  −
1200
A
20 m
4- In the figure shown below, the incline is frictionless and the mass m falls with acceleration 4.0
m/s2. (Ignore the friction and the mass of pulley). If the tension in the cord connecting the two
masses is T= 16 N
a) Find the angle θ of the incline.
Σ FX = T − m ′ g sin θ = m ′ a
16 − 2 (10) sin θ = 214
θ = 23.5°
(2)
2 kg
m
θ
b) Find the mass m of the falling body.
Σ Fy = m g − T = m a
T = m (g − a ) ⇒16 = m (10 − 4 )
m = 2.67 kg
(2)
5- Two blocks are placed one on the top of the other as shown in the figure. A force F is applied to
the lower block. If the coefficients of friction between the lower block and the surface are
μ s = 0.50 and μ k = 0.25,
a) What value of F is needed to put the block into motion?
(2)
F = f smax = µ S (m1 + m2 ) g
F = 0.5 (2 + 3)10 = 25 N
2 kg
F
3 kg
b) If F= 20 N, what is the magnitude of the frictional force.
(1)
f s = F = 20 N
6- A space station of diameter 80 m is turning about its axis at a constant rate. If the acceleration of
the outer rim of the station is 2.5 m/s2,
a) Find the speed of the station
(1)
v2
⇒ v = ar = 2.5 (40)
r
v = 10 m / s
ar =
b) What is the period of revolution of the space station?
(1)
v=
2π r
2 π r 2(3.14 ) 40
⇒T =
=
T
v
10
T = 24.8 s
c) How many revolutions per minute does the station make?
(1)
1
60
f= ⇒ f=
= 2.4 rpm
24.8
T