Molecular Physics | Thermodynamics Answers

A pair of eyeglass frame is made of epoxy plastic. At room temperature of 23.4 oC, the

frames have circular lens 2.3cm in radius.

(a) Show that if the frames are heated to fit the lenses 2.32cm in radius, the temperature

required is given by

𝑇 = 𝑇𝑜 +

1

𝛼 (𝐿𝐿

𝑜 − 1)

With α the coefficient of linear expansivity of epoxy plastic.

(b) The coefficient of epoxy plastic is 1.3 x 10-4 oC-1

Calculate the temperature at which the 2.32cm lenses would be fitted into the frames.

An iron railway line is 30m long at a temperature of 27oC. What would be the length of the 

railway line when the temperature increases to 57oC? The coefficient of linear expansion of 

iron is 1.2 x 10-5 oC-1

A 2.0-g particle moving at 6.2 m/s makes a perfectly elastic head-on collision with a resting 1.0-g object.

(a) Find the speed of each particle after the collision.

2.0 g particle ___    m/s

1.0 g particle ___   m/s

(b) Find the speed of each particle after the collision if the stationary particle has a mass of 10 g.

2.0 g particle  ___   m/s

10.0 g particle ___   m/s

(c) Find the final kinetic energy of the incident 2.0-g particle in the situations described in parts (a) and (b).

KE in part (a) ___  J

KE in part (b) ___    J

Consider a frictionless track as shown in the figure below. A block of mass m₁ = 5.55 kg

 is released from . It makes a head-on elastic collision at  with a block of mass m₂ = 12.5 kg

 that is initially at rest. Calculate the maximum height to which m₁ rises after the collision.

___m

A spaceship's orbital maneuver requires a speed increase of 1.35 ✕ 10³ m/s. If its engine has an exhaust speed of 2.25 ✕ 10³ m/s, determine the required ratio M_i/M_f

 of its initial mass to its final mass. (The difference M_i − M_f

 equals the mass of the ejected fuel.)

____.

A bullet of mass m = 8.00 g is fired into a block of mass M = 150 g that is initially at rest at the edge of a table of height h = 1.00 m (see figure below). The bullet remains in the block, and after the impact the block lands d = 2.30 m from the bottom of the table. Determine the initial speed of the bullet.

___ kg/s

Three ice skaters meet at the center of a rink and each stands at rest facing the center, within arm's reach of the other two. On a signal, each skater pushes himself away from the other two across the frictionless ice. After the push, skater A with mass m_A = 70.0 kg

 moves in the negative y-direction at 2.00 m/s and skater B with mass m_B = 85.0 kg

 moves in the negative x-direction at 3.50 m/s. Find the x- and y-components of the 75.0 kg skater C's velocity (in m/s) after the push.

v_Cx=__ m/s

v_Cy=___ m/s

Squids are the fastest marine invertebrates, using a powerful set of muscles to take in and then eject water in a form of jet propulsion that can propel them to speeds of over 11.5 m/s. What speed (in m/s) would a stationary 2.00 kg squid achieve by ejecting 0.115 kg of water (not included in the squid's mass) at 3.50 m/s? Neglect other forces, including the drag force on the squid.

___m/s

The front 1.20 m of a 1,250-kg car is designed as a "crumple zone" that collapses to absorb the shock of a collision.

(a) If a car traveling 26.0 m/s stops uniformly in 1.20 m, how long does the collision last?

___ s

(b) What is the magnitude of the average force on the car?

 ___N

(c) What is the magnitude of the acceleration of the car? Express the acceleration as a multiple of the acceleration of gravity.

 ___ g

A tennis player receives a shot with the ball (0.0600 kg) traveling horizontally at 58.0 m/s and returns the shot with the ball traveling horizontally at 36.8 m/s in the opposite direction. (Take the direction of the ball's final velocity (toward the net) to be the +x-direction.)

(a) What is the impulse delivered to the ball by the racket?

magnitude ___ N · s

(b) What work does the racket do on the ball? (Indicate the direction with the sign of your answer.)

 ___J