Problem#1
A force F applied to an object of mass m1 produces an acceleration of 3.00 m/s2. The same force applied to a second object of mass m2 produces an acceleration of 1.00 m/s2. (a) What is the value of the ratio m1/m2? (b) If m1 and m2 are combined, find their acceleration under the action of the force F.Answer:
For the same force F, acting on different masses
F1 = m1a1 and F2 = m2a2
(a) the value of the ratio
m1/m2 = a2/a1 = 1/3
(b) F = (m1 + m2)a = 4m1a
a = ¼ a1 = 0.75 m/s2
Problem#2
The largest-caliber antiaircraft gun operated by the German air force during World War II was the 12.8-cm Flak 40. This weapon fired a 25.8-kg shell with a muzzle speed of 880 m/s. What propulsive force was necessary to attain the muzzle speed within the 6.00-m barrel? (Assume the shell moves horizontally with constant acceleration and neglect friction.)
Answer:
Given:
vf = 880 m/s
xf = 6 m
m = 25.8 kg
we use
vf2 = vi2 + 2a(xf – xi) and a = F/m, then
vf2 = 2(F/m)(xf – xi)
(880 m/s)2 = 2(F/25.8 kg)(6 m – 0)
F = 1.66 x 106 N
Problem#3
A 3.00-kg object undergoes an acceleration given by a = (2.00i + 5.00j) m/s2. Find the resultant force acting on it and the magnitude of the resultant force.
Answer:
Given:
m = 3.00 kg,
a = (2.00i + 5.00j) m/s2
ΣF = ma = (3.00 kg)(2.00i + 5.00j) m/s2 = (6.00i + 15.0j) N
then the magnitude of the force F is
F = [(6.00)2 + (15.0)2]1/2 = 16.2 N
Problem#4
The gravitational force on a baseball is -Fgj. A pitcher throws the baseball with velocity vi by uniformly accelerating it straight forward horizontally for a time interval Δt = t – 0 = t. If the ball starts from rest, (a) through what distance does it accelerate before its release? (b) What force does the pitcher exert on the ball?
Answer:
Given:
Fg =weight of ball = mg
vrelease = v and time to accelerate = t :
a = Δv/Δt = (v/t)i
(a) Distance is
x = vavt = (v/2)t
(b) force does the pitcher exert on the ball is
Fp – Fgj = (Fgv/gt)i
Then
Fp = Fgj + (Fgv/gt)i
Problem#5
To model a spacecraft, a toy rocket engine is securely fastened to a large puck, which can glide with negligible friction over a horizontal surface, taken as the xy plane. The 4.00-kg puck has a velocity of 300i m/s at one instant. Eight seconds later, its velocity is to be (8.00i + 10.0j) m/s. Assuming the rocket engine exerts a constant horizontal force, find (a) the components of the force and (b) its magnitude.
Answer:
Given:
m = 4.00 kg
vi = 3.00i m/s
vf = (8.00i + 10.0j) m/s at t = 8.0 s
we use
a = Δv/t = [(5.00i + 10.0j) m/s]/8.0 s = (0.625i + 1.25j) m/s2
then
F = ma = (4.00 kg)(0.625i + 1.25j) m/s2
F = (2.50i + 5.00j) N
And
F = [(2.5)2 + (5.0)2]1/2 = 5.59 N
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