Quizzes
Chapter 1
Problem A
A barrel has a radius of 20.0 in, a height of 25.0 in, and a mass of 600.0 mg. What is its total mass (in kg) if it is filled with benzene? The density of benzene is 0.87873 gm/cm3?
Solution:
Volume of cylinder = π r2 h
= 3.14 (20.0 in)2 (25.0 in) (2.54 cm/1 in)3 = 515 x 10 3 cm3
Mass =density x volume
= (0.87873 g/cm3) (1 kg/1000 g) (515 x 103 cm3) = 452.15 kg
Therefore, total mass = 452.15 kg + 0.6 kg = 452.75 kg ~ 453 kg
Problem B
What is the mass (in kg) of a lead semi-sphere of radius 5.0 in? (Density of lead is 11.342 g/cm3)
Solution:
Volume of semi-sphere = (0.5) (4/3) π r3
= (2/3) (3.14) (5.0 in)3 (2.54 cm/1 in)3 = 4287.948 cm3
Mass = density x volume
= (11.341 gm/cm3) (1 kg/ 1000 g) (4287.948 cm3) = 48.63 kg ~ 49 kg.
Chapter 2
Problem 1
The position of a particle in meters is described as x(t) = 6t2 - 4t +3
(a) What is vavg in the period from t = 0 s to t = 5 s?
(b) What is v at t = 3 s?
(c) What is the acceleration when the particle stops momentarily?
Solution:
(a) vavg = (Δx/Δt)
= [x(t=5) - x(t=0)] / (5-0) = (130 m) / (5 s) = 26 m/s
(b) v = dx/dt = 12 t - 4
v at (t = 3 s) is 32 m/s
(c ) The particle stops momentarily when v = 0,
i.e., 12 t - 4 = 0 gives t = 0.33 s
However, we find from the equation (a = dv/dt = 12 m/s2)
that the acceleration is always constant (at every moment).
Problem 2
A) A stone is thrown upward from the top of a building with an initial speed of 1 m/s. If the building is 20-m high what is the velocity of the stone when it his the bottom?
B) Solve it also when the stone is thrown downward with initial velocity 1 m/s?
Solution:
A) Initial conditions: v0 = +1 m/s
a = - g = - 9.8 m/s2
y0 = 0 m (if we take the origin coordinate where the motion starts)
y = - 20 m
v2 = v02—2g(y– y0) = (1 m/s)2—2 (9.8 m/s2)(-20 m)
v = 19.8 m/s downward
B) Initial conditions: v0 = -1 m/s
a = - g = - 9.8 m/s2
y0 = 0 m (if we take the origin coordinate where the motion starts)
y = - 20 m
v2 = v02—2g(y– y0)
= (-1 m/s)2—2 (9.8 m/s2)(-20 m)
v = 19.8 m/s downward ( same answer)