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Jogger runs 1km north, 5km west, and then a further 2km to the south-west in a total time of 45 minutes.
(a) draw an accurate scale diagram to find the jogger's resultant displacement vector and find both magnitude and direction.
A 3.00 m long steel wire is fixed in a ceiling and a mass of 12.3 kg is hanging from the wire. The wire has a diameter d = 0.80 mm, a Young’s modulus 2.00 GPa and mass density 7860 kg/m3 .
(a) Calculate the stress in the wire.
(b) Calculate the strain.
(c) Calculate the elongation of the wire.
(d) Calculate the transverse speed of pulse.
(e) Calculate the longitudinal sound speed.
Determine the magnitude P of the force which the man must exert perpendicular to the handle of the high – pressure washer in order to cause loss of contact at the front support B. note that the operator prevents movement of the wheel with his left foot. The 60-Kg machine has its mass center at point G. Treat the problem as two – dimensional.
what is the gauge pressure at the bottom of a freshwater pool that is 12.5 ft deep?
a) Derive an expression for the logarithmic decrement of a damped oscillator.
b) A block attached to a spring is made to oscillate with initial amplitude
of 8.0 cm. After 2.2 minutes, the amplitude decreases to 5.0 cm. Calculate
(i) the time when the amplitude becomes 2.0 cm, and (ii) the value of damping
constant gamma for this motion.
c. A sound wave of frequency 300 Hz travels with speed 340ms-1 along
the negative x-direction. Each point of the medium moves up and down through a
total distance of 5.0 mm. Determine the necessary parameters to represent the
wave mathematically.
a. The orbit of a satellite about the Earth is given by r= 10000 /(1+0.6cos theta)
What is the eccentricity and shape of the orbit? Also calculate the apogee and
perigee distances.
b. A steel ball A collides elastically with another steel ball B (at rest initially) and the
ball B is observed to move off at an angle theta with the initial direction of motion of A.
The mass of B is five times that of A. Determine the direction in which A moves
after collision and the speeds of the two balls.
c. The displacement of an object executing simple harmonic oscillations is given by:
x = 0.02 sin 2pie (t+0.01) m
Determine (a) amplitude of the oscillatory motion, (b) time-period of oscillation,
(c) maximum velocity, (d) maximum acceleration, and (e) initial displacement of
the object.
a. A child of mass 30 kg slides from rest down a wooden pole by a distance of
3.0 m. Calculate the average force of friction acting on the child if her speed is
2.0 ms-1 when she hits the ground. Take g=10 ms-2
b. The average angular acceleration of a stone lodged in a rotating car wheel is
100 rads-2. What will the stone’s final angular speed be after 3.0 s, if it starts
from rest? Also calculate its angular displacement during this time.
c. A star having rotational inertia of 10 x1048 kgm2 is rotating at an angular speed
of 2.0 revolutions per month about its axis. The only force on it is the force of
gravitation. When its nuclear fuel is exhausted, it shrinks to a neutron star
having rotational inertia of 6.0 x1048 kgm2 Determine the angular speed
of the neutron star in revolutions per month.
a - A child of mass 30 kg travels in a lift. Calculate the force exerted on the child by
the floor of the lift when the lift moves (i) downward with an acceleration of 1.0 ms-2 , (ii) upward with an acceleration of 1.0 ms-2 What is the weight of the
child when the lift falls freely? Take g = 10 ms-2
b- A satellite of mass 200 kg is displaced by a distance of 2Refrom a point on the
Earth’s surface, where Re is the radius of the Earth. Calculate the work done on
the satellite by the force of gravitation. Take the values of the constants in your
calculation from the astrophysical data given in the course.
a -A box of mass 10 kg is pulled by a mass-less rope with a force of 40 N. The rope
makes an angle of 30deg with the horizontal. Draw the free-body diagram showing
all forces on the box. Determine the acceleration of the box if the coefficient of
kinetic friction between the floor and the box is 0.2. Take g =10 ms-2 .
b-A ball of mass 100 g strikes a wall with the speed 2.0 ms-1 and bounces off the
wall in the opposite direction with the same speed. Calculate the impulse of the
ball.
A student is pulling a 11.0 kg sled along flat ground. The students 30.0 kg sister then sits in the sled. The student then applies a 430 N force at an angle of 35° N of E. If the force of friction is 180 N, what is the acceleration of the sister sitting in the sled. (Ensure you draw a free body diagram.)
