A disc with radius 0.060 m and rotational inertia 0.061 kg.m^2 has a rope wrapped around its parameter. The other end of the rope is holding a 0.20 kg mass. The mass is held at 1.0 m above the floor. You release the mass from rest. This causes the disc to spin and the mass to fall. How long does it take the mass to fall to the ground?

Hint: use torque and angular acceleration.

A solid sphere of radius 0.13 m and mass 0.25 kg rolls down an incline plane without slipping. If the incline plane is 0.40 m tall and has an angle of 24° then how long does it take the sphere to roll down the incline plane?

Hint: rotational inertia of a solid sphere is 2/5*(mr^2).

A girl of mass mG is standing on a plank of mass mP. Both are originally at rest on a frozen lake that constitutes a frictionless, flat surface. The girl begins to walk along the plank at a constant velocity vGP to the right relative to the plank. (The subscript GP denotes the girl relative to the plank.)

(a) What is the velocity vPI of the plank relative to the surface of the ice? (Use the following as necessary: vGP, mG, and mP. Indicate the direction with the sign of your answer. Let the positive direction be in the direction that the girl walks.)

vPI =

(b) What is the girl's velocity vGI relative to the ice surface? (Use the following as necessary: vGP, mG, and mP. Indicate the direction with the sign of your answer. Let the positive direction be in the direction that the girl walks.)

vGI =

A girl swings back and forth on a swing with ropes that are 4.00m long. The maximum height she reaches is 2.10m above the ground. At the lowest point of the swing, she is 0.500m above the ground.

What is the girl

To improve the stability of vehicles many roads have banked curves. Discuss the direction of acceleration and the forces acting on a car going around a circular banked curve with constant speed.

A factory emits steam into the air. How could those same water molecules eventually reside in the ocean? In a river? In groundwater? In a bear's body?

Using the arguments based on quantum mechanics and the Boltzmann energy distribution
explain briefly:
a) why real molecules behave (from the thermodynamics point of view) as the ideal gas molecules?
b) Why are the rotational degrees of freedom activated at lower temperatures for most molecules?
c) Why are the vibrational degrees of freedom activated at high temperatures for most molecules?
d) Why are the noble gases well approximated by the ideal gas?

You pour a glass of orange juice and realize it is warm (24 Celsius). You find the mass of the orange juice to be 642 grams. A quick search shows the specific heat of orange juice is about 3770J/(kg*C). You add ice cubes from the freezer which you assume are at 0 Celsius. if you add a single 50 gram cube of ice, what is the final temperature of the mixture? How many ice cubes do you need to add before the juice reaches 0 celsius?

A lunch tray is being held in one hand, as the drawing illustrates. The mass of the tray itself is 0.200 kg, and its center of gravity is located at its geometrical center. On the tray is a 1.00 kg plate of food and a 0.150 kg cup of coffee. Obtain the force T exerted by the thumb and the force F exerted by the four fingers. Both forces act perpendicular to the tray, which is being held parallel to the ground.

This week we will discuss the following topics:

1. Rotational Dynamics : Angular displacement, Angular velocity, angular acceleration.

2. Rigid Body and Moment of Inertia

3. Angular Momentum, conservation of Angular Momentum and Torque with some examples of applications.

4. Mechanical Equilibrium and conditions of equilibrium

5. Elasticity, Plasticity and Hooke's Law

6. Parallel Forces and net torque

7. Coefficient of Elasticity, stress and strain.

The cable of the 1800 kg elevator cab in the figure snaps when the cab is at rest at the first floor, where the cab bottom is a distance d = 4.9 m above a spring of spring constant k = 0.33 MN/m. A safety device clamps the cab against guide rails so that a constant frictional force of 3.2 kN opposes the cab's motion. (a) Find the speed of the cab just before it hits the spring. (b) Find the maximum distance x that the spring is compressed (the frictional force still acts during this compression). (c) Find the distance (above the point of maximum compression) that the cab will bounce back up the shaft. (d) Using conservation of energy, find the approximate total distance that the cab will move before coming to rest.

(Assume that the frictional force on the cab is negligible when the cab is stationary.)

A 0.320 kg puck at rest on a horizontal frictionless surface is struck by a 0.220 kg puck moving in the positive x direction with a speed of 4.05 m/s. After the collision, the 0.220 kg puck has a speed of 1.29 m/s at an angle of ? = 60.0° counterclockwise from the positive x axis.

(a) Determine the velocity of the 0.320 kg puck after the collision. Express your answer in vector form.

vf = ___m/s

(b) Find the percent of kinetic energy lost in the collision.

100*?K/Ki = ___%

An object with a size r₀ has a Reynolds number of 4 when it moves through a fluid at a speed v₀. What is the Reynolds number for an object with a size 2r₀ moving through the same fluid at a speed v₀/2?

The answer is 4. Please explain why and what concepts were used to get to this answer!!!

Study Guide 1

1. A child sitting 1.70 m from the center of a merry-go-round moves with a speed of 1.85 m/s, Calculate the centripetal acceleration of the child and the net horizontal force exerted on the child. (mass m = 22.5 kg )

2. A horizontal force of 320 NN is exerted on a 2.0-kg ball as it rotates (at arm's length) uniformly in a horizontal circle of radius 0.90 m, Calculate the speed of the ball.

3. Two objects attract each other gravitationally with a force of 2.3×10⁻¹⁰ N when they are 0.65 mm apart. Their total mass is 4.6 kg, Find their individual masses.

4. Calculate the speed of a satellite moving in a stable circular orbit about the Earth at a height of 4840 km

5. A satellite of mass 5430 kg orbits the Earth and has a period of 6570 s . Determine the radius of its circular orbit, the magnitude of the Earth's gravitational force on the satellite, and the altitude of the satellite.

All answers with units included

Using the minimal action principle obtain the equation of motion of the free particle from the relativistic Lagrangian.

(i) Define in words the strength of an electric field at a given point in space.

(ii) An electron experiences an acceleration of magnitude 2.0 × 10¹³ ms⁻² in the positive x-direction, due to a uniform electric field. Calculate the magnitude and direction of the electric field.