Preliminary Physics 1 (PHS1014)
Tutorial 5
1.
A 1300 N crate rests on a floor. How much work is required to move it at a constant speed.
a. 4 m along the floor along the floor against a frictional force of 230 N. (9.2 × 10 2 J)
b. 4 m vertically. (5.2× 103 J )
2.
A box of mass 5.00kg is accelerated from rest across a floor at a rate of 2ms -2 for 7.0 s . Find the net work done on
the box. (4.9 × 102 J)
3.
A 55kg hiker starts at an elevation of 1600 m and climbs to the top of a 3300 m peak.}
a.
b.
c.
What is the hikers change in potential energy? (9.2× 105 J)
What is the minimum work required for the hiker?
Can the actual work done be more than this? Explain why
4.
A 1400 kg sports car accelerates from rest to 95 km/hr in 7.4 s. What is the average power delivered by the engine?
(6.6 × 10 4 W)
5.
A pump is to lift 18.0 kg of water per minute through a height of 3.6 m. What output rating (watts) should the pump
motor have? ( 10.6 W)
6.
The graph shown below Shows the variation of the displacement x with time t for a body of mass 500g
executing s.h.m.
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
What is the periodic time of the oscillation?
What is the frequency of the oscillation?
What is the angular frequency?
What is the amplitude of the motion?
At what times will the object have maximum and minimum velocities?
What are the maximum and minimum values of the kinetic energies and at what times do they
occur?
Calculate the maximum speed of the mass.
Calculate the maximum acceleration of the mass.
Calculate the maximum force acting on the mass.
Calculate the velocity of the mass at x = 10 cm.
Sketch graphs to show how velocity varies with time.
l.
m.
n.
Sketch graphs to show how the kinetic and potential energy varies with time.
Write an equation to show how the velocity varies with time.
State one way in which the shape of the graph would change if there was a small amount of
damping.
7.
a.
Define simple harmonic motion
b. If you double the amplitude of a simple harmonic oscillation how does the
following change:(i)
Frequency
(ii)
Maximum Velocity
(iii)
Maximum Acceleration
(iv)
Total Mechanical Energy
Use equations to justify your answers.
c.
8.
Define resonance. Describe illustrating the description with a suitable graph
of the effect of progressively increasing damping on a resonant vibration.
A spring is stretched 0.120 m when a 0.38 kg mass is placed on it. The spring
is then stretched an additional 0.10 m from the equilibrium point and then
released. Determine:
a.
the amplitude of the oscillation.
b.
the spring constant.
c.
the maximum velocity.
d.
the maximum acceleration.
e.
the equation of the velocity as a function of time.
9.
A 100g mass vibrates on a spring with a maximum displacement of 45mm, if the displacement is zero at t
= 0 and frequency of 8.0 Hz. Determine the:
a. amplitude in SI unit.
b. angular frequency
c. spring constant.
d. displacement equation of the motion.
e. maximum potential energy.
f. displacement at 40ms.
10. If you half the mass of a simple harmonic oscillator how does this change the:
a.
frequency
b.
the maximum acceleration.
c.
the total energy
d.
amplitude
Explain with the help of equations.
11. A mass of 0.500 kg is placed on a vertical spring and the spring stretches by 16 cm. If the spring is then
pulled down an additional 10cm and released, find :
a.
the spring constant.
b.
angular frequency
c.
the maximum acceleration of the mass.
12. State the conditions necessary for simple harmonic motion (SHM).
13. A 0.60 kg mass vibrates in SHM according to the equation:
x(t )
a.
b.
c.
d.
e.
0.35 cos(20.5 t ) where x is in meters and t is in seconds. Determine the
amplitude
frequency
total energy
kinetic energy when x = ¼ of the amplitude.
graph for 2 cycles of the wave above (label graph completely).
14. A 500g mass vibrates in SHM according to the equation:
x(t )
a.
b.
c.
d.
e.
f.
0.24 sin 12.40t
3
, Where x is in centimeters and t is in seconds. Determine
the:
amplitude
frequency
total energy
displacement when after 3 seconds.
potential energy when x = 15cm.
kinetic energy when x = 40% of the amplitude.
15. A 750g mass vibrates in SHM according to the equation: x (t )
meters and t is in seconds. Determine the:
a. amplitude
b. period
c. total energy
d. displacement when after 475ms.
e. potential energy when x = 8cm.
f. kinetic energy when x = -½ of the amplitude.
g. total energy
0.25 cos 4.0 t
5
, Where x is in