Figure 5-28 shows four choices for the direction of a force of magnitude F to be applied to a block on an inclined plane. The directions are either horizontal or vertical. (For choice b, the force is not enough to lift the block off the plane.) Rank the choices according to the magnitude of the normal force acting on the block from the
plane, greatest first.
The rank of normal force by inclined surface due to the application of force a, b, c, and d from greatest to least is .
Angle is given .
The problem is based on Newton’s second law of motion which states that the acceleration of an object is dependent on the net force acting upon the object and the mass of the object. Draw free-body diagrams for each force separately and resolve the given force and weight. Using components of forces the net force equation can be written.
The calculation for normal due to application of force a:
Due to the application of force, there is no motion in the vertical direction, so the net force is zero.
The equation for the net force can be written as,
The calculation for normal due to application of force b:
The calculation for normal due to application of force c:
Similarly, the net force equation for force c,
The calculation for normal due to application of force d:
Similarly, the net force equation for force d,
From equations (1), (2), (3), and (4) we get,
Forces a, b, c, and d have the same magnitude then the increasing order of normal forces is .
Two horizontal forces,
pull a banana split across a frictionlesslunch counter. Without using acalculator, determine which of thevectors in the free-body diagram ofFig. 5-20 best represent (a) and(b) . What is the net-force componentalong (c) the x axis and (d) the yaxis? Into which quadrants do (e) thenet-force vector and (f) the split’s accelerationvector point?
July 17, 1981, Kansas City: The newly opened Hyatt Regency is packed with people listening and dancing to a band playing favorites from the 1940s. Many of the people are crowded onto the walkways that hang like bridges across the wide atrium. Suddenly two of the walkways collapse, falling onto the merrymakers on the main floor.
The walkways were suspended one above another on vertical rods and held in place by nuts threaded onto the rods. In the original design, only two long rods were to be used, each extending through all three walkways (Fig. 5-24a). If each walkway and the merrymakers on it have a combined mass of M, what is the total mass supported by the threads and two nuts on (a) the lowest walkway and (b) the highest walkway?
Apparently, someone responsible for the actual construction realized that threading nuts on a rod is impossible except at the ends, so the design was changed: Instead, six rods were used, each connecting two walkways (Fig. 5-24b). What now is the total mass supported by the threads and two nuts on (c) the lowest walkway, (d) the upper side of the highest walkway, and (e) the lower side of the highest walkway? It was this design that failed on that tragic
night—a simple engineering error.
A car that weighs is initially moving at role="math" localid="1656996519190" when the brakes are applied and the car is brought to a stop in role="math" localid="1656996543045" . Assuming the force that stops the car is constant, find (a) the magnitude of that force and (b) the time required for the change in speed. If the initial speed is doubled, and the car experiences the same force during the braking, by what factors are (c) the stopping distance and (d) the stopping time multiplied? (There could be a lesson here about the danger of driving at high speeds.)
Imagine a landing craft approaching the surface of Callisto, one of Jupiter’s moons. If the engine provides an upward force (thrust) of 3260N, the craft descends at constant speed; if the engine provides only 2200 N, the craft accelerates downward at. (a) What is the weight of the landing craft in the vicinity of Callisto’s surface? (b) What is the mass of the craft? (c) What is the magnitude of the free-fall acceleration near the surface of Callisto?
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