GS 103, 4 questions

1. If you eat 500 calories per day(roughly one large order of fries) above your energy needs, how long will it take to gain 20 pounds? How long would you have to walk (assuming you burned 80 calories per mile walked) to burn off those 20 pounds?

2. Which has more gravitational potential energy: a

200-kilogram boulder 1 meter off of the ground, a 50-kilogram boulder 4-meters

off the ground, or a 1-kilogram rock 200 meters off the ground? Which of these

can do the most work if all of the potential energy was converted to kinetic

energy?

3. Compared a car (mass of 2000 kg) moving at 10

miles per hour, how much kinetic energy (in Joules) does that same car have

when it moves at 20 miles per hour? At 50 miles per hour? 75 miles per hour?  (Hint: you will need to convert to miles per

hour to meters per second).

4. Using your results from question 9, create a graph

of those results. What does your graph suggest to you about the difficulty of

stopping a car as its speed increases?

Answers

1. different studies suggest that the energy content of one pound of body weight is equivalent to 3500 calories. This means that 20 pounds are equivalent to 20*3500 = 70000 calories. If you eat an extra 500 calories per day the number of days necessary to take 20 pounds is 70000/500 = 140 days. if one burns 80 calories per mile then to burn 20 pounds (or 70000 calories) one needs to walk 70000/80 = 875 miles in total or per day 875/140 = 6.25 miles/day

2. The potential energy is DEFINED as $E p =m*g*h$ where m is the mass, g is the gravitational acceleration, h is the height

a) $E p =200*9.8*1 = 1960$ J

b) $E p =50*9.8*4 = 1960$ J

c) $E p =1*9.8*200 = 1960$ J

In all the cases the potential energy is the same

3. The kinetic energy is defined as $E c = m*v^2/2$ where m is the mass and v is the speed.

a) $10 miles/hour = 10*1609/3600 =4.47 meter/second$

$Ec1 =2000*4.47^2/2 =  19980.9 J$

b) $20 miles/hour = 20*1609/3600 = 8.94 meter/second$

$Ec2 = 2000*8.94^2/2 = 79923.6 J$

$Ec2/Ec1 = 4 times$

c) $50 miles/hour =50*1609/3600 = 22.35 meter/second$

$Ec3 =2000*22.35^2/2 = 499522.5 J$

$Ec3/Ec1 = 25 times$

d) $75 miles/hour =75*1609/3600 =33.52 meter/second$

$Ec4 = 2000*33.52^2/2 = 1123590.4 J$

$Ec4/Ec1 = 56.25 times$

4. For the graph see attached file. From the graph one can say the the difficulty of stopping a moving car increases as the square of its speed. The graph is a parabola.