Chapter 7: Q5CQ (page 177)
Can kinetic energy be negative? Explain
Kinetic energy cannot be negative.
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A cart is set rolling across a level table, at the same speed on every trial. If it runs into a patch of sand, the cart exerts on the sand an average horizontal force of 6N and travels a distance of through the sand as it comes to a stop. If instead the cart runs into a patch of gravel on which the cart exerts an average horizontal force of 9N, how far into the gravel will the cart roll before stopping? (a) 9cm (b) 6cm (c) 4cm (d) 3cm (e) none of those answers.
Let represent the direction horizontally north, represent northeast (halfway between north and east), and so on. Each direction specification can be thought of as a unit vector. Rank from the largest to the smallest the following dot products. Note that zero is larger than a negative number. If two quantities are equal, display that fact in your ranking. (a) (b) (c) (d) (e) .
(i) Rank the gravitational accelerations you would measure for the following falling objects: (a) a 2-Kg object 5 cm above the floor, (b) a 2 Kg object 120 cm above the floor, (c) a 3 Kg object 80 cm above the floor, and (d) a object above the floor. List the one with the largest magnitude of acceleration first. If any are equal, show their equality in your list. (ii) Rank the gravitational forces on the same four objects, listing the one with the largest magnitude first. (iii) Rank the gravitational potential energies (of the object–Earth system) for the same four objects, largest first, and taking y = 0 at the floor.
Can a normal force do work? If not, why not? If so, give an example.
In a control system, an accelerometer consists of a 4.7 g object sliding on a calibrated horizontal rail. A low-mass spring attaches the object to a flange at one end of the rail. Grease on the rail makes static friction negligible, but rapidly damps out vibrations of the sliding object. When subject to a steady acceleration of
, the object should be at a location away from its equilibrium position. Find the force constant of the spring required for the calibration to be correct.
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