MCAT Question of the Day

What is the half-life of a radionuclide if 1/16 of its initial mass is present after 2 hours?

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B.

In every half-life, the mass decreases to half its previous value:

1/16 = 1/2⁴

It takes four half-lives to decay down to 1/16 the original mass. Each must be 30 minutes long since the entire process takes two hours.

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A 70 kg construction worker accidentally pushes a 100kg block of metal alloy off a 8 meter high stand. The block lands on top of a stake partially put into the ground, driving it completely into the dirt.

What is the kinetic energy of the block just before striking the stake? (The previous question revealed the final velocity of the block was 12.5 m/s.)

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B.

E = (1/2)mv2 = (1/2) (100kg) (12.5 m/s)2
E = 7840 J

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A construction worker accidentally pushes a 100kg block of metal alloy off a 8 meter high stand. The block lands on top of a stake partially put into the ground, driving it completely into the dirt.

What is the velocity of the block just before striking the stake? Ignore air resistance.

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C.

Vf2 = Vi2 + 2ax = 0 + 2 (9.8 m/s2)(8 m)
V = 12.5 m/s

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Monochromatic light passes through two parallel slits in a screen and falls on a piece of film. The pattern produced is an example of:

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B.

The light passing through each slit is diffracted (bent), and the two resulting beams overlap on the film to form interference patterns.
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A ball with a mass of 1.0 kg sits at the top of a 30o incline plane that is 20.0 meters long. If the potential energy of the ball is 98 J at the top of the incline, what is the potential energy once it rolls half way down the incline?

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B.

Since the height is decreasing, the E_p is decreasing and must have a value less than its initial reading 98 J. D is eliminated because its value is higher than the initial E_p value. C is eliminated because its value is the same as the initial value of the E_p. A is eliminated because the only way to have zero E_p is if the body is at ground level. That leaves B as the only option.

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