MCAT Question of the Day

Correct Answer: D. 30N.

Since the object is not moving, its acceleration must be zero, so the net force on it must also be zero. Therefore, the magnitude of the buoyant force upward must equal the magnitude of the weight downward, the specific gravity is extraneous information:

B = w = mg = (3 kg)(10 N/kg) = 30 N

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Correct Answer: B. 30^o.

Pressure is force over area. The cross-sectional area of the of the circulatory system is not changing. The direction of the force appears to be changing. But the blood is still flowing orthogonal to the area, creating the same pressure due to the heart. The only additional element is that gravitational force is being applied.

This additional gravitation force opposes the heart force by a factor of sin(theta) times its weight. We are told that the blood acceleration is equal to g. All we need to find now is when the sin is equal to one half. This will yield a pressure of one half of the horizontal value. This occurs at 30^o.

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Correct Answer: A. 4F

Keeping Coulomb’s law in mind, if you reduce the distance by 1/2, then the force increases by the inverse squared of 1/2 which is 4 times. Note the question is only asking about the magnitude of the forces as opposed to their directions. If the direction were asked, then the sign of the charge (i.e. positive or negative) would matter.

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Correct Answer: A. -5/4Q

The basic principle: the spheres are equal in size so when they touch (conduction of charge), the charge will be split equally between the 2 spheres (this is consistent with the Conservation of Charge). When the spheres are separated, each sphere will retain 1/2 of the charge (because they are identical in size).

1) X plus Y: When -Q touches +2Q, the overall charge of the 2 spheres would be -Q + 2Q = +Q but that charge is shared with 2 spheres so each sphere has a +1/2Q charge.

2) new X plus Z: Now +1/2 Q – 3Q = -5/2Q and half of this is -5/4Q

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Correct Answer: D. A and B

In the situation described, there are 3 vectors and each of the 3 vectors are perpendicular to each other (you can imagine the relationship as being the x, y and z axes, or as governed by the right hand rule): the current (I), the electric field (F) and the magnetic field (B). The latter encircles the current carrying wire.

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Correct Answer: A. Twice as much work is done on the smaller mass.

PHY 5.3

Simple way:

Use the Work-Energy Theorem where the variation of the kinetic energy of a system is equal to the work of the net force applied to the system. Thus the work is just the change in kinetic energy (i.e. final MINUS initial). But the final is 0 because the final velocity is 0 (at “rest”). So we get:

Work = -m(v²)/2

Looking at the equation, it is clear that doubling the velocity has a greater impact on the work as compared to doubling the mass.

Side Note: Friction always does negative work because it is opposite to the direction of motion. Similarly, work must be negative in this problem.

Alternate method:

Work = Force times distance (actually, displacement) = m (a) x

To determine the acceleration a (actually, the deceleration):

V² = Vo² + 2ax = 0 (each object has a final vel. of 0)

a = – (Vo²)/2x

Work = m [- (Vo²)/2x] x = -m(Vo²)/2

Now by testing the numbers given, you can see that the original velocity has a greater impact than the mass.

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Correct Answer: A. M^-1L³T^-2

PHY 2.4

This is a classic example of dimensional analysis (DA). Expect to use DA to one degree or the other during the real MCAT. First, you should know that the unit of force is a newton which is also a kg m/s² (even if you did not memorize that, it is easy to work out since F = ma so the units of F must be kg multiplied by acceleration which is m/s²). Of course the 2 m’s in the Law of Gravitation represent masses (M) and the r represents a distance or length (L). So we get:

F = G(m1m2/r²)

Now transferring to the fundamental quantities except for G:

MLT^-2 = G(M)²L^-2

Divide both sides by (M)²L^-2 and isolate for G:

G = M^-1L³T^-2

… which is the same as m³kg^-1s^-2.

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Correct Answer: A. 17 MHz

If the antenna is 1/4 the wavelength of the broadcasting wave, then the broadcasting wave must be 4 x 4 meters = 16 meters.

The velocity of electromagnetic radiation = 3.0 x 10⁸ m/s

Velocity = (wavelength)(frequency)

Frequency = (3.0 x 10⁸)/(16) = (30 x 10⁷)/(15) approximately

= 2 x 10⁷ Hz = 20 x 10⁶ Hz = 20 MHz approximately (Mega is the SI prefix for 10⁶).

List of equations to memorize for the MCAT: www.goldstandard-mcat.com/physics-equation-lists/

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Correct Answer: D. both the temperature and pressure of the gas.

The word “kinetic” means movement or motion. An increase in motion means that there is an increase in kinetic energy which we know is directly related to temperature (CHM 4.1.2). When there is an increase in motion, that means there is an increase in the force of the molecules hitting the walls of the container. Pressure is force per unit area (PHY 6.1.2) so the pressure must increase if the motion increases.

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Correct Answer: C. Initial buoyant force < maximum buoyant force

Tricky! You must recognize that the half immersed block would submerge as long as its density is greater than 1/2 the density of water or a specific gravity of 0.5. Thus this block may: (i) have a specific gravity between 0.5 and 1.0 (which means the block’s density would be less than that of water); or (ii) it could have a density equal to that of water; but (iii) it could NOT have a density greater than that of water (this would make it sink to the bottom but the question says that it remains afloat so (iii) is not possible): nonetheless, it would submerge from a position of being held half immersed [thus answer choice B. is not the best answer because of the preceding points (i) and (ii)]. When the block sinks, it will certainly displace more water than it did initially; therefore, the buoyant force increases to its maximum. {cf. Archimedes Principle}

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