Classical Mechanics Answers

You throw a ball with a speed of 25.0 m/s at an angle of 40.0◦ above the horizontal directly toward a
wall, as shown in Fig. 3.3. The wall is 22.0m from the release point of the ball. (a) How long does the
ball take to reach the wall? (b) How far above the release point does the ball hit the wall? (c) What
are the horizontal and vertical components of its velocity as it hits the wall? (d) When it hits, has it
passed the highest point on its trajectory?

A steel cylinder of cylinder of 500mm outside diameter and 200mm inside diameter is set in rotation
about its axis. If the cylinder is 900mm long, of density 7800kg/m3
, calculate the torque required to
give an angular acceleration of 0.5rad/s2
.

Dr. P’s grandfather clock has a pendulum of length of 1.0 cm. Determine: (a) its period on earth, (b) its
period on the moon where g = 1.62 m/s2.

A planet of mass M moves along a circle around the Sun with velocity v = 34.9 km/s (relative to the heliocentric reference frame). Find the period of revolution of this planet around the Sun.

A certain color emerges at 15° in the first-order spectrum. At what angle would this same color emerge in the second order if the same source and grating are used?

One strategy in a snowball fight is to throw
a snowball at a high angle over level ground.
While your opponent is watching this first
snowball, you throw a second snowball at a
low angle and time it to arrive at the same
time as the first.
Assume both snowballs are thrown with
the same initial speed 34 m/s. The first snowball is thrown at an angle of 53◦
above the
horizontal. At what angle should you throw
the second snowball to make it hit the same
point as the first? Note the starting and ending heights are the same. The acceleration of
gravity is 9.8 m/s
2
.

A shell acquires the initial velocity v = 320 m/s, having made n = 2.0 turns inside the barrel whose length is equal to l = 2.0 m. Assuming that the shell moves inside the barrel with a uniform acceleration, find the angular velocity of its axial rotation at the moment when the shell escapes the barrel.

Explain briefly why the ruled lines must coincide with the centre of the table and must face the
telescope. (Hint: consider the effect on the results if this was not the case).

A certain color emerges at 15° in the first-order spectrum. At what angle would this same color
emerge in the second order if the same source and grating are used?

Suppose that you are given a monochromatic light source of wavelength 600 nm, and a diffraction
grating with 500 lines.mm1
. How many full orders will be visible for a normal incidence
experiment? (Hint: the maximum possible angle for diffraction is 90°).