Question

A 2000-lb car drives from Denver (altitude: 5280 feet) to Los Angeles (sea level). What is its change in potential energy, in BTU? g = 32.174 ft/s² Provide your answer rounded to one decimal place, and make sure to include units. *

2) The velocity of an object increases by 50% (V₂=1.5 V₁). By what factor does the kinetic energy increase? *
1
4
1.5
2.25

Answer 1

1) -13570.3 Btu

2) 2.25

Step-by-step explanation:

The formula for potential energy is:

`E_p = m*g*h`

Where m is the mass in slugs, g is the gravity and h is the change in height. Soliving the equation:

`E_p = 2000lb*(1 slug)/(32.174 lb) *32.174 (ft)/(s^2) *(0ft-5280ft) = -10560000 lbf*ft * (1 Btu)/(778.17 lbf*ft) = -13570.3 Btu`

The car would lose -13570.3 Btu in potential energy.

2) The kinetic energy is given by:

`E_k = (1)/(2) mv^2`

Then:

`(E_k_2)/(E_k_1) = ((1)/(2)mv_2^2)/((1)/(2)mv_1^2)  = ((1)/(2)m(1.5v_1)^2)/((1)/(2)mv_1^2)=1.5^2(v_1^2)/(v_1^2) = 2.25`