Answers and Explanations

Part 8: Mechanical Comprehension (MC)

1. 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).

2. D

   Work is accomplished when force is applied against an object. This is summarized by the formula W = Fd where F is force in newtons (N), d is distance in meters (m), and W is work in joules (J).

3. B

   The smaller pulleys always turn faster than larger pulleys in a system.

4. A

   Any work that is done to accelerate an object at rest to speed v will be converted into the kinetic energy of that object. This principle is known as the work-energy theorem.

5. D

   Performing work at the rate of 1 joule per second is the same as expending 1 watt of power.

6. C

   There are several properties of liquids that are unchanging. First, they are effectively incompressible. Even when extremely high pressure is applied to a liquid, the volume of the liquid will decrease only a very small amount. This property makes liquids very effective for transmitting force. And the second overarching principle of hydraulics is that liquids conform themselves to the shape of their container. Whether in a pipe or a pump, liquids will always change their shape to fill the space completely. But not all liquids are by nature good lubricants.

7. C

   The force of static friction can increase in response to an applied force, resisting movement, but only up to a maximum value. If the applied force is greater than the maximum value of static friction, the crate will move. Since the applied force is given, the maximum force of static friction is what needs to be calculated. The force of static friction has a maximum value equal to the product of the normal force and the coefficient. The coefficient is given, but the normal force is not. However, since the object is at rest on a flat, horizontal surface, the normal force will be equal and opposite to the object’s weight. Therefore F_N = 250 N. The maximum force of static friction then is: F_fs = (0.8)(250) = 200 N. The applied force is 200 N, but the maximum force of static friction is also 200 N. Since friction always opposes movement, it is opposite the applied force, so the net force can be calculated like this: F_net = (200 N) + (−200 N) = 0 N. Since the net force is zero, the object will not move. Another way to put it is that the applied force is enough to take the resisting static friction to its limit, but not enough to overcome it.

8. B

   Using the formula for pressure , if 100 pounds of force are applied over an area of 2 square inches, then the resulting pressure is 50 pounds per square inch (psi).

9. D

   Mechanical advantage is defined as “the advantage gained by the use of a mechanism in transmitting force.” Using the proper equipment, it is possible to increase or even multiply force many times over what is initially applied.

10. C

    The fulcrum is the point that the lever pivots on. The position of the fulcrum will define whether any mechanical advantage is gained. If the fulcrum is closer to the object being lifted, less effort is required to do the work.

11. B

    Based on Newton’s second law, F = ma, rearrange the equation for acceleration: . Units of force must be in Newtons and mass in kg. Taking 30 N and dividing by 5 kg equals 6 .

12. C

    According to Newton’s Second Law of Motion, when a net force acts on an object, the object will accelerate in the direction of the net force. The acceleration will be less if the mass of the object is greater. (A) is not necessarily true. An object may speed up or slow down when a net force acts on it depending on the direction of the force and the object’s initial motion. The cumulative force is the same as the net force, so (B) does not make much sense. As for (D), in uniform circular motion, speed (magnitude) is constant, but the direction of motion changes constantly. Thus the net force applied leads to acceleration but no change in speed.

13. A

    Belted pulleys, unlike meshed gears, turn in the same direction.

14. A

    The illustration shows a fixed pulley.

15. C

    The load piston has a total surface area of 10 square inches. Using the formula , 100 pounds ÷ 10 square inches = 10 pounds per square inch (psi) of pressure that should be applied to the load piston.

16. C

    Forces are vector quantities, which means they have both magnitude and direction. The 30 N and 50 N forces are acting in opposite directions on the horizontal dimension. Since 50 N > 30 N, it will dominate and the resultant is: 50 N − 30 N = 20 N in the direction of the greater force (i.e., to the left). There is nothing opposing the 10 N force, so the result is 10 N acting vertically downward.

17. D

    Note that in order to lift the load 1 foot, it is necessary to pull the rope a total of 4 feet. This is because each of the four rope links must shorten by 1 foot to get the lower block to move 1 foot. Neglecting friction, this gives a total mechanical advantage of 4:1, so if 4 pounds of force are required to lift a load, only 1 pound needs to be applied to the rope.

18. A

    A child’s teeter-totter is an example of a first-class lever because the fulcrum is located between the load and the applied force.

19. C

    In the example of the hockey puck sliding along an ice surface, while ice has much less friction than most surfaces, it will still exert a sliding frictional force on the puck that eventually causes it to stop moving.

20. A

    Torque is twisting force. When a bolt is being tightened, torque is being applied to the bolt. For example, when tightening a fastener, if a wrench is used that is 1 foot long, and a force of 100 pounds applied to the end of the wrench in a direction perpendicular to the wrench, 100 foot-pounds (ft-lb) of torque is being applied.

21. B

    When tightening a fastener, if a person uses a wrench that is 1 foot long, and applies a force of 100 pounds to the end of the wrench, 100 foot-pounds (ft-lb) of torque is being applied. Simply multiply the applied force by the length of the wrench to determine the torque.

22. C

    A 50 N weight will produce a 50 N force acting downward. Since the system is in equilibrium, the upward tension force must exactly balance the downward weight, which gives a tension of 50 N acting upwards.

23. A

    The pulleys of a block-and-tackle system multiply the force exerted in pulling the rope of the system by the number of pulleys in the system. Therefore, the lifting force that the pulleys exert on the object is the force exerted in pulling the rope multiplied by the number of pulleys used.

24. A

    According to Newton’s Gravitational Law, since gravity exerts a force on bodies that pulls them together, this force causes an acceleration due to gravity, which is represented by the symbol g.

25. C

    The fulcrum is the point on which a lever pivots.