Part A = 3.08*10^-14

If a drop is to be deflected a distance d = 0.320 mm by the time it reaches the end of the deflection plate, what magnitude of charge q must be given to the drop?

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An infinitely long line of charge has a linear charge density of 8.00*10^−12 C/m. A proton is at distance 19.0 cm from the line and is moving directly toward the line with speed 1200 m/s.

How close does the proton get to the line of charge?

Part A = L = ((0.5 * x_{c}^2 * k) – m * g * sin(θ) * x_{c}) / (m * g * (sin(θ) + cos(θ)*μ))

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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 x_{c}. 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 x_{c} while inside of the gun). Use g for the magnitude of acceleration due to gravity.

Part A = u = sqrt((2 * V * q) / m)

Part B = m/q = (R * B_{0})^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 B_{0} 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 = x_{2} = d / sqrt(2kH / mg)

Part B = x_{2} = (x_{1} * d) / (d – d_{12})

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 x_{1} and finds that the marble falls short of its target by a horizontal distance d_{12}.

By what distance, x_{2}, 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 x_{2} that depends only on X_{1} and distance measurements.

Part A = k = 2.5/0.005

Part B = 0.37 m

The following chart and accompanying graph depict an experiment to determine the spring constant for a baby bouncer.

What is the spring constant of the spring being tested for the baby bouncer?

One of the greatest difficulties with setting up the baby bouncer is determining the right height above the floor so that the child can push off and bounce. Knowledge of physics can be really helpful here.

If the spring constant k = 5.0 * 10^2 N, the baby has a mass m = 11 kg, and the baby’s legs reach a distance d = 0.15 m from the bouncer, what should be the height of the “empty” bouncer above the floor?

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