Question

2. Suppose a car travels 108 km at a speed of 20.0 m/s, and uses 2.20 gallons of gasoline. Only 30% of the gasoline goes into useful work by the force that keeps the car moving at constant speed despite friction. (The energy content of gasoline is 1.3 ✕ 10⁸ J per gallon.)

(a) What is the force exerted to keep the car moving at constant speed?
N

(b) If the required force is directly proportional to speed, how many gallons will be used to drive 108 km at a speed of 28.0 m/s?
gallons

3.(a) Calculate the force needed to bring a 900 kg car to rest from a speed of 95.0 km/h in a distance of 105 m (a fairly typical distance for a nonpanic stop).
N
(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), i.e. find the ratio of the force in part(b) to the force in part(a).
(force in part (b) / force in part (a))

4.A car's bumper is designed to withstand a 6.48-km/h (1.8-m/s) collision with an immovable object without damage to the body of the car. The bumper cushions the shock by absorbing the force over a distance. Calculate the magnitude of the average force on a bumper that collapses 0.300 m while bringing a 840-kg car to rest from an initial speed of 1.8 m/s.
N

5.a) How much gravitational potential energy (relative to the ground on which it is built) is stored in an Egyptian pyramid, given its mass is about 9 ✕ 10⁹ kg and its center of mass is 46.0 m above the surrounding ground?
J
(b) What is the ratio of this energy to the daily food intake of a person (1.2 ✕ 10⁷ J)?
:1

6.In a downhill ski race surprisingly little advantage is gained by getting a running start. This is because the initial kinetic energy is small compared with the gain in gravitational potential energy even on small hills. To demonstrate this, find the final speed and the time taken for a skier who skies 70.0 m along a 35° slope neglecting friction for the following two cases. (Note that this time difference can be very significant in competitive events so it is still worthwhile to get a running start.)

(a) starting from rest
final speed
m/s
time taken
s

(b) starting with an initial speed of 2.50 m/s
final speed
m/s
time taken
s

7.A 3.00 ✕ 10⁵ kg subway train is brought to a stop from a speed of 0.500 m/s in 0.900 m by a large spring bumper at the end of its track. What is the force constant k of the spring?
N/m

8.A 70.0 kg skier with an initial speed of 10.0 m/s coasts up a 2.50 m high rise as shown in Figure 6.23. Find his final speed at the top, given that the coefficient of friction between her skis and the snow is 0.0800. (Hint: Find the distance traveled up the incline assuming a straight-line path as shown in the figure.)
m/s

9. A person in good physical condition can put out 100 W of useful power for several hours at a stretch, perhaps by pedaling a mechanism that drives an electric generator. Neglecting any problems of generator efficiency and practical considerations such as resting time:

(a) How many people would it take to run a 4.00 kW electric clothes dryer?
people
(b) How many people would it take to replace a large electric power plant that generates 800 MW?
people

10.(a) What is the efficiency of an out-of-condition professor who does 2.00 ✕ 10⁵ J of useful work while metabolizing 490 kcal of food energy?
%
(b) How many food calories would a well-conditioned athlete metabolize in doing the same work with an efficiency of 20%?
kcal

Answer 1

2 Sol: given: d=108km 2 108x109 m v=20mis volume (V) = 2.2 gal Eg = 1.3 X10% degal n = 30% ra). Actual Energy provided by gasoline is E-EX(V) = (1.3460°)2-2) E = 2.86x10J -> work done by engine will be [W=Fxd (also w=nE] So, nE=Fxd > F= n€ = 30%)2-86X10€) 108x103 F=794.40] (b) As said the ratio's are proportional de É V = F = F(W) 5.794.4%28 - 20 F = 1112.20

f' is the force required, so the energy required will be E'=Fd - 1112,2x108x10% 10.–4.0048103 30% E'= 4.00uxlo' Now, the volume, using Energy provided by gasoline per literis V'= E'lEg = 4.004x109/634108 Tv' = 3.08 gal] Hope for VOTE Thank you -