Part A = See the screenshot
Consider an infinite sheet of parallel wires. The sheet lies in the xy plane. A current l runs in the -y direction through each wire. There are N/a wires per unit length in the x direction.
Write an expression for B(d),the magnetic field a distance d above the xy plane of the sheet.Click for More...
Part A = 455.165 km
Part B = 8.9523 g
Part C = 3.1107 g
Consider a bird that flies at an average speed of 10.7 m/s and releases energy from its body fat reserves at an average rate of 3.70 W (this rate represents the power consumption of the bird). Assume that the bird consumes 4g of fat to fly over a distance db without stopping for feeding. How far will the bird fly before feeding again?
How many grams of carbohydrate mcarb would the bird have to consume to travel the same distance db?
Field observations suggest that a migrating ruby-throated hummingbird can fly across the Gulf of Mexico on a nonstop flight traveling a distance of about 800 km. Assuming that the bird has an average speed of 40.0 km/hr and an average power consumption of 1.70 W, how many grams of fat does a ruby-throated hummingbird need to accomplish the nonstop flight across the Gulf of Mexico?
Part A = T1 = (cos(θ1) * m * g) / sin(θ1 + θ2)
A chandelier with mass m is attached to the ceiling of a large concert hall by two cables. Because the ceiling is covered with intricate architectural decorations (not indicated in the figure, which uses a humbler depiction), the workers who hung the chandelier couldn’t attach the cables to the ceiling directly above the chandelier. Instead, they attached the cables to the ceiling near the walls. Cable 1 has tension T1 and makes an angle of θ1 with the ceiling. Cable 2 has tension T2 and makes an angle of θ2 with the ceiling.
Find an expression for T1, the tension in cable 1, that does not depend on T2.Click for More...
Part A = L = ((0.5 * xc^2 * k) – m * g * sin(θ) * xc) / (m * g * (sin(θ) + cos(θ)*μ))
Click for more info and a screenshot
A block of mass m is placed in a smooth-bored spring gun at the bottom of the incline so that it compresses the spring by an amount xc. The spring has spring constant k. The incline makes an angle θ with the horizontal and the coefficient of kinetic friction between the block and the incline is μ. The block is released, exits the muzzle of the gun, and slides up an incline a total distance L.
Find L, the distance traveled along the incline by the block after it exits the gun. Ignore friction when the block is inside the gun. Also, assume that the uncompressed spring is just at the top of the gun (i.e., the block moves a distance xc while inside of the gun). Use g for the magnitude of acceleration due to gravity.Click for More...
Part A = u = sqrt((2 * V * q) / m)
Part B = m/q = (R * B0)^2 / 2V
J. J. Thomson is best known for his discoveries about the nature of cathode rays. Another important contribution of his was the invention, together with one of his students, of the mass spectrometer. The ratio of mass m to (positive) charge q of an ion may be accurately determined in a mass spectrometer. In essence, the spectrometer consists of two regions: one that accelerates the ion through a potential V and a second that measures its radius of curvature in a perpendicular magnetic field. The ion begins at potential V and is accelerated toward zero potential. When the particle exits the region with the electric field it will have obtained a speed u.
With what speed u does the ion exit the acceleration region?
After being accelerated, the particle enters a uniform magnetic field of strength B0 and travels in a circle of radius R (determined by observing where it hits on a screen–as shown in the figure). The results of this experiment allow one to find m/q in terms of the experimentally measured quantities such as the particle radius, the magnetic field, and the applied voltage. What is m/q?
Part A = x2 = d / sqrt(2kH / mg)
Part B = x2 = (x1 * d) / (d – d12)
Two children are trying to shoot a marble of mass m into a small box using a spring-loaded gun that is fixed on a table and shoots horizontally from the edge of the table. The edge of the table is a height H above the top of the box (the height of which is negligibly small), and the center of the box is a distance d from the edge of the table. The spring has a spring constant k. The first child compresses the spring a distance x1 and finds that the marble falls short of its target by a horizontal distance d12.
By what distance, x2, should the second child compress the spring so that the marble lands in the middle of the box? (Assume that height of the box is negligible, so that there is no chance that the marble will hit the side of the box before it lands in the bottom.)
Now imagine that the second child does not know the mass of the marble, the height of the table above the floor, or the spring constant. Find an expression for x2 that depends only on X1 and distance measurements.