Physics Help?

Question

1. A man jumps a fence 2.45 m. If the PEg at the top point of his trajectory was 1.59 * 10^3 J, what was his mass?

a) 666 kg

b) 662 kg

c) 66.2 kg

d) 26.6 kg

 

2. You slide a 5-kg object up a ramp inclined at 25 degrees. How long is the ramp if the PEg of the object is 2.4 × 10^2 J?

a) 32

b) 12

c) 22

 

3. A 100,000-lb freight car is drawn 2500 ft up a long a 1.2% grade at constant speed. Find the work done against gravity.

a) 4067400 J

b) 2940000 J

c) 3000000 J

d) 0 N

Answer 1

1. PE_g = mgh = 1590J

m(9.8)(2.45) - 1590

m = 66.22 kg

One of the numbers must be wrong.  You can also guess the answer by knowing that a typical man usually weights above 40 kg and seldom weighs more than 100 kg

 

2. PE_g = mgh = 240

plugging in given values

5(9.8)h = 240

we find

h = 4.9m

if the incline is 25° , then sin25° = opp/hyp = h/ramp length

ramp length = h/sin25° = 11.58 m

 

3. work done against gravity is PEg = mgh

convert height in ft to meters

h = 0.012(2500)(.3048) = 9.144m

convert pounds to kg

100000 lb = 45359 kg

PE_g = 45359*9.8*9.144 = 4,064,674J

 

Answer 2

1. Remember that potential energy is equal to mass x gravity x height. (PEg=mgh)

 

At the top of the fence h=2.45 meters, and his potential energy is = 1.59x10^3 J.

 

If you use the equation, you get 1.59x10^3 = m(9.81m/s^2)(2.45m), solving this for m, you should get 66.2 kg.

 

2. Again, PEg=mgh. First solve for h using the information your already know --> 2.4x10^2=(5kg)(9.81m/s^2)h.

Once you get h, you have the opposite side of your ramp (which is a right triangle) and you can solve for the length of the ramp (the hypotenuse) using sin(25)=opposite/hypotenuse.

 

3.W=mgh.

 

Your height is equal to 1.2% of  2500 ft, which is equal to 30 ft.

Your mass is equal to 100,000 lbs.

Before you can plug these into the equation you have to convert them into meters and kg, respectively (since these are the units of Joules).

This gives 100,000 lb = 45,359.2 kg and 30 ft = 9.144 m

Plug these in to get W= (45,359.2 kg)(9.144 m)(9.81 m/s^2) = ~4,067,400.