question: a 2.1 x 10^3 kg car starts from rest at the top of a driveway that is sloped at an angle of 20.0 degrees with the horizontal. an average friction force of 4.0 x 10^3 N implodes the car's motion so that the car's speed at the bottom of the driveway is 3.8 m/s. What is the length of the driveway?
(question involves work-kinetic thm)
answer: 5.1m
how do you get this answer?
2007-10-30 11:57:37 · 1 answers · asked by Haya 1 in Science & Mathematics ➔ Physics
Let us say that the unknown length of the driveway is L. Then the top of the driveway is at an elevation of L*sin(theta), where theta is the given angle of 20 degrees. So the car initially has gravitational potential energy of GPE = mgh = mgL*sin(theta), where m is the given mass of the car and g is the acceleration due to gravity. At the bottom of the driveway, the car no longer has any potential energy, but it does have kinetic energy of KE = 0.5*mv^2, where v is the given velocity. Due to conservation of energy, we can say KE_f = GPE_0 + W, where the _f subscript indicates "final" and _0 indicates "initial," and W is the work done on the system. In this case, the only work was done by friction and will be negative. The work done by friction will be -FL, where F is the magnitude of the friction force. So 0.5mv^2 = mgL*sin(theta) - FL, where L is the only unknown. I get L = 4.99 m, not 5.1 m. I got the same answer when I solved using net force and acceleration instead, so I think the answer you were given is wrong.
2007-11-02 05:25:23 · answer #1 · answered by DavidK93 7 · 0⤊ 0⤋