Answers and Explanations

Mechanical Comprehension Practice Questions

  1. A

    The work-energy theorem states that work performed on an object will increase the object’s mechanical energy by the amount of work applied to the object. In this case the increase in mechanical energy was the additional potential energy resulting from the object being lifted higher. Therefore the final PE equals the work.

  2. B

    Since F = ma, then a = . Change in velocity = acceleration × time. Therefore: .

  3. B

    This block and tackle has 2 pulleys, so the mechanical advantage is 2:1, because the weight will only move half the distance that the rope is pulled. As a result, the force applied will be half the weight, or 12 lbs.

  4. D

    Although the mass and time are unknown, they are not needed to solve the problem. When the ball is 5 m above the ground all its energy is PE, but when it hits the ground all its energy is KE. Since energy is conserved, set PE = KE or . The mass cancels out and, since the question asks for the approximate speed, g = 10 will suffice. 2 × 10 × 5 = v2 and 100 = v2, so v = 10.

  5. D

    Work = Force × Distance or 2000 × 5 = 10,000 J.

  6. C

    To calculate power, start by determining the work performed. Since there are 20 parts that weigh (exert a downward force) 10 N each that are lifted 2 m, work = 20 × 10 × 2 = 400 J. The machine accomplishes this work in 2 seconds. Power is , or 200 watts.

  7. D

    Pressure is force divided by the area over which it is applied, so

  8. C

    This could be solved with two different approaches. Gear A makes 14 revolutions and has 15 teeth, so 14 × 15 = 210 teeth would pass any point. Since gear B has 10 teeth, it would need to make 21 revolutions to match the teeth of gear A. Alternatively, the gear ratio is 3:2, so the proportion could be used to obtain the same answer, 21.

  9. B

    The mechanical advantage of a wheel and axle is equal to the ratios of the radii of the two wheels. The problem states that the smaller wheel’s diameter is m, so its radius is m and the ratio of the two radii is 10:1.

  10. A

    The cross-section of a kitchen knife is very small on the cutting side and gets thicker toward the top, just as a wedge does.

  11. B

    Due to the mechanical advantage that is provided by the block and tackle, the distance that the object will move for a given amount of rope pulled is decreased in proportion to the mechanical advantage provided. Therefore, to keep the rate of lifting the object constant between the simple pulley and the block and tackle, Person X will need to pull the rope faster than Person Y but will use less force.

  12. D

    Torque (T) is determined by multiplying a force (F) by the lever arm length (L) that the force is acting through or T = F × L. In this case, to achieve an applied torque of 50 ft-lb, with a 2 ft lever arm, (where F = T/L), 50ft-lb/2ft = 25 lb of force is needed.

  13. A

    Based on Newton’s second law, F = ma, where F = force in newtons, m = mass in kilograms, and a = acceleration in m/s2. Therefore, rearranging the equation for mass, you get: m = . Since you know that friction is not negligible, you also know that the resultant force will be less than 10 N (see diagram below). Therefore, the maximum mass possible, in a frictionless system is calculated by dividing 10 N by 10 m/s2, which gives 1 kg. Knowing that friction will diminish the applied force, the resulting mass has to be less than 1 kg, which matches answer choice (A).

    Resultant Force = 10 N – force of friction

    Thus, the resultant force will be less than 10 N.

  14. D

    Kinetic friction is exhibited when surfaces/objects move past one another. The normal force, which is a factor of the weight of the object, will affect friction (for example: move your hand across a table lightly and then again with more force; increased force leads to increased friction). The nature and area of the surfaces in contact with each other will also affect the friction that develops between two surfaces (for example: moving your hand across a desk with oil on it is a lot easier than with honey; also, moving one finger across a desk develops less friction than moving your entire hand). The speed at which the surfaces move past each other however, does not impact the frictional forces (though it may generate more heat).

  15. D

    Weight = gm, where g = gravitational acceleration (m/s2) and m = mass in kg. On Xendor, the gravitational acceleration is 3 times as much as on Earth, giving a new g of approximately 30 m/s2. To calculate weight on Xendor, multiply the new gravitational acceleration by the person’s mass: Weight = 30 m/s2 × 100 kg = 3000 N.

  16. C

    Recall that W = Fd, where W is work in joules, F is force in newtons and d is distance in meters. Therefore, rearranging the equation for force, you get: F = . Taking 80 J and dividing by 2 m, you get 40 N.