A heavy sled is being pulled by two people as shown in the figure. The coefficient of static friction between the sled and the ground is μs = 0.571, and the kinetic friction coefficient is μk = 0.395. The combined mass of the sled and its load is m = 306 kg. The ropes are separated by an angle φ = 23°, and they make an angle θ = 29.7° with the horizontal.

Assuming both ropes pull equally hard, what is the minimum rope tension required to get the sled moving?

If this rope tension is maintained after the sled starts moving, what is the sled\'s acceleration?

An airplane is heading due south at a speed of 680 km/h .

A. If a wind begins blowing from the southwest at a speed of 90 km/h (average), calculate the velocity (magnitude) of the plane relative to the ground.

B. Calculate the velocity (direction) of the plane relative to the ground.

C. Calculate how far from its intended position will it be after 18 min if the pilot takes no corrective action.

A rod AB with A at the origin rotates such that the angle between the rod and the x?axis is theta = pi (8t

A charge q1 = 5.00 nC is placed at the origin of an xy-coordinate system, and a charge q2 = -4.50 nC is placed on the positive x axis at x= 4.00 cm . If a third charge q3 = 8.00 nC is now placed at the point x= 4.00 cm , y= 3.00 cmcm find the x and y components of the total force exerted on this charge by the other two charges. Find Fx, Fy, and find the magnitude and direction of F.

Solar energy is an alternative to fossil fuels for providing electrical power for both homes and businesses. It may be locally produced and used at the same location as the panels, which reduces distribution costs. Large facilities may be located in available space and the power added to the "grid" that distributes electricity. Solar power may be a better choice in rural or undeveloped areas where the grid infrastructure is unreliable or just not there, and it has been discussed as an alternative for reconstruction in storm-damaged Puerto Rico. It is also useful in less sunny areas, and here in Kentucky the regional power provider is developing a shared solar energy farm to supplement its conventional power plants. Even the Coal Museum in eastern Kentucky has solar panels to provide building power. 1. The Sun provides approximately 1.4 kilowatts (kW) of energy adding all the light striking one square meter perpendicular to a line to the Sun above the Earth's atmosphere. If solar panels are 25% efficient in converting this optical energy to electrical energy, and if they are oriented to make maximum use of incident sunlight, how much panel area is needed to develop 10% of the regional power production which is 3.5 gigawatts (GW) while the Sun shines? (3.5 GW is 3,500 MW. Currently LG&E has a 10 MW solar farm covering 50 acres.) 2. A typical single solar panel that would be installed on a home uses crystalline silicon as the material that creates the current, measures 1x2 meters, and produces 340 watts at 48 volts. It is said to be 17% efficient, allowing that not all the sunlight at the top of the atmosphere reaches the surface, and that some wavelengths are beyond the range over which silicon responds. How many of these panels would be needed to supply 15 kW that would fulfill the peak needs of a typical home? What area of the roof would they cover? This is for peak use, but typically the average power needs are about 5 kW. 3. If it is sunny 8 hours a day, then you would need 3X as many panels and a way to store energy to use them 24/7, but storage also allows you have fewer panels to meet peak needs. Allowing that the panels gather enough energy during 8 hours to provide power for that time and for 16 more hours, how much energy has to be stored? Consider two alternatives: pumped water and Tesla batteries. If you could pump water to a height of 20 meters, say to a pond or pool up the hill from your home, how much water by volume would have to be moved to store this energy . (Use the potential energy of gravity, mgh, to figure this out. ) For batteries, consider the Tesla "Powerwall", a module that stores 13.5 kWh of energy and provides 7 kW peak AC power. 4. Given what you know about the physics of solar, comment on the viability of it as a sole source of power for your home, and your rechargeable electric car. If you have a clever way of storing energy, mention it here too.

You have been employed by the local circus to plan their human cannonball performance. For this act, a spring-loaded cannon will shoot a human projectile, the Great Flyinski, across the big top to a net below. The net is located 4 m lower than the muzzle of the cannon from which the Great Flyinski is launched. The cannon will shoot the Great Flyinski at an angle of 45 degrees above the horizontal and at a speed of 15 m/s. The ringmaster has asked you to determine a few things in order to make sure the show is both safe and entertaining.

a) The x-component of the human cannonball’s initial velocity and final are  _____ m/s.

b) The y-component of the human cannonball’s initial velocity and final are _____ m/s.

c) Now, report the final speed of the human cannonball when he hits the net. The ringmaster will use this information to make sure she uses a strong enough net, as her circus has had problems with previous human cannonballs breaking through the bottom of the nets, and it has not been well-received.

d) How long is the human cannonball in the air? The ringmaster wants to make sure the human cannonball is in the air long enough to impress the audience.

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?