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Chapter 7: Q6 CQ (page 258)
When solving for speed in Example 7.4, we kept only the positive root. Why?
We keep only the positive root of the speed because speed cannot be negative.
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Jogging on hard surfaces with insufficiently padded shoes produces large forces in the feet and legs.
(a) Calculate the magnitude of the force needed to stop the downward motion of a jogger鈥檚 leg, if his leg has a mass of 13.0 kg, a speed of 6.00 m/s, and stops in a distance of 1.50 cm. (Be certain to include the weight of the 75.0-kg jogger鈥檚 body.)
(b) Compare this force with the weight of the jogger.
(a) How high a hill can a car coast up (engine disengaged) if work done by friction is negligible and its initial speed is 110 km/h?
(b) If, in actuality, a 750-kg car with an initial speed of 110 km/h is observed to coast up a hill to a height 22.0 m above its starting point, how much thermal energy was generated by friction?
(c) What is the average force of friction if the hill has a slope 2.5掳 above the horizontal?
(a) What force must be supplied by an elevator cable to produce an acceleration of 0.800 m/s2 against a 200-N frictional force, if the mass of the loaded elevator is 1500 kg?
(b) How much work is done by the cable in lifting the elevator 20.0 m?
(c) What is the final speed of the elevator if it starts from rest?
(d) How much work went into thermal energy?
In Example 7.7, we calculated the final speed of a roller coaster that descended \(20{\rm{ m}}\) in height and had an initial speed of \(5{\rm{ m}}/{\rm{s}}\) downhill. Suppose the roller coaster had had an initial speed of \(5{\rm{ m}}/{\rm{s}}\) uphill instead, and it coasted uphill, stopped, and then rolled back down to a final point 20m below the start. We would find in that case that it had the same final speed. Explain in terms of conservation of energy.
(a) Calculate the force needed to bring a 950-kg car to rest from a speed of 90.0 km/h in a distance of 120 m (a fairly typical distance for a non-panic stop).
(b) Suppose instead the car hits a concrete abutment at full speed and is brought to a stop in 2.00 m. Calculate the force exerted on the car and compare it with the force found in part (a).
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