Classical Mechanics Answers

Two blocks of masses m₁=1.7 kg and m₂=3.7 kg are put on a frictionless horizontal surface. A spring of stiffness k=970 N/m and negligible mass is placed between the blocks and they are pushed together to compress the spring by distance d from its equilibrium length. The configuration is fixed by a cord that holds the blocks. When the cord is burned, the first block moves to the left with a speed of v₁=1.9 m/s. Calculate the initial compression of the spring, d. 

A 47.0 kg student starts from rest and slides 26.0 m down a hill where the average force of friction is 55.0 N. What is the final speed of the student at the bottom of the hill if the vertical drop was 17.0 m?

Use the following information to answer the next 2 questions:

A 25.0-kg child in Red Deer pumps herself on a swing when she kicks upward on the downswing, thus changing the distance from the pivot point to her centre of gravity from 2.40 m to 2.28 m.

1) The resonant frequency of her swing before the kick is: ___ Hz. 

2) The resonant frequency of her swing after the kick is: ___ Hz.

In the statements listed below, fill in the blanks with the best answer listed ont the bottom. Note that some answers may be used more than once!

3) Engineers build energy ________ systems into buildings so that an earthquake will not destroy them easily.

4) The periodic push that a child exerts on the swing must match the ________ frequency of the swing.

5) Compared to audible sound, the frequency of earthquake waves are generally very ________.

6) Every oscillating system has a ________ frequency, which is determined by the physical properties of the object.

1.forced

2.resonant

3.high

4.low

5.damping

Use 9.81m/s² for gravity if needed!

1) The magnitude of the restoring force that acts on a 1.0-kg pendulum when it is displaced 2.0° from equilibrium is ___ N. 

2) The magnitude of the restoring force that acts on a 1.0-kg pendulum when it is displaced 10.0° from equilibrium is ___ N. 

3)  On earth the period of a 1.50-m pendulum is ___s.

4) On the hypothetical planet Xeon, a pendulum with a length of 95.0 cm swings with a frequency of 1.50 Hz. The acceleration due to gravity on Xeon is ___ m/s².

5) A pendulum is swinging back and forth:

Which of the following factors affect the period of the pendulum:

I. length

II. mass

III. angle of release

IV. accleration due to gravity

A- I only

B- I and II

C- III and IV

D- I and IV

It is required to project a body from a point on level ground in such a way

as to clear a thin vertical barrier of height h placed at a distance a from the

point of projection. Show that the body will just skim the top of the barrier

if

ga2

2u

2



tan2 α − a tan α +

ga2

2u

2

+ h



= 0

where u is the speed of projection and α is the angle of projection above the

horizontal