Question

# Can i please get some help with this homework. The only one i got right was Question #1 which is why I didn't

include it. However, I have gotten everyone after it wrong. Can you please explain to me how to do each of these problems. I will be heading to bed after I post because i just got off a 12hr shift and will be heading back to work at 3pm tomorrow i will get up in the morning and review this post and most likely be asking you about some of these problem if i don't understand how you came up with some of the answer or if i can't follow the steps. Thank you very much for your help in advance.

2.Suppose a car travels 108 km at a speed of 40.0 m/s, and uses 1.90 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 **✕** 10^{8} 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 800 kg car to rest from a speed of 85.0 km/h in a distance of 130 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 5.40-km/h (1.5-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 0.255 m while bringing a 940-kg car to rest from an initial speed of 1.5 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 7 **✕** 10^{9} kg and its center of mass is 31.0 m above the surrounding ground?

J

(b) What is the ratio of this energy to the daily food intake of a person (1.2 **✕** 10^{7} 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 60.0 m along a 30° 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 2.00 m/s

final speed

m/s

time taken

s

7.A 6.00 **✕** 10^{5} kg subway train is brought to a stop from a speed of 0.500 m/s in 0.600 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 65.0 kg skier with an initial speed of 13.0 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 3.00 kW electric clothes dryer?

people

(b) How many people would it take to replace a large electric power plant that generates 500 MW?

people

10.(a) What is the efficiency of an out-of-condition professor who does 2.30 **✕** 10^{5} J of useful work while metabolizing 510 kcal of food energy?

%

(b) How many food calories would a well-conditioned athlete metabolize in doing the same work with an efficiency of 15%?

kcal