Conservation energy question 2 A car is rolling down a ramp that is inclined at

Question

Conservation energy question 2

A car is rolling down a ramp that is inclined at and angle of 9.9 degree with respect to horizontal. There is no friction acting from the road on the tires. Employ Newton's Law to find the speed of a car that starts from rest and rolls down the ramp a distance of 52 m. A car is rolling down a ramp that is inclined at and angle of 9.2 degree with respect to horizontal. There is no friction acting from the road on the tires. Employ conservation of mechanical energy to find the speed of a car that starts from rest and rolls down the ramp a distance of 49 m. You drive your 1.369-kg car at a constant speed of 15 mph a distance of 54 m down a ramp that has a grade of 11 %. Use conservation of energy to find the work done by the frictional force acting from the road on the tires. Define positive direction in the forward direction.

Explanation / Answer

Here ,

A) theta = 9.9 degree

distance , d = 52 m

let the speed of car is v

Using conservation of energy

0.5 * m * v^2 = m * g * L * sin(theta)

0.5 * v^2 = 9.8 * 52 * sin(9.9)

v = 13.2 m/s

the speed of the car is 13.2 m/s

B)theta = 9.2 degree

distance , d = 49 m

let the speed of car is v

Using conservation of energy

0.5 * m * v^2 = m * g * L * sin(theta)

0.5 * v^2 = 9.8 * 49 * sin(9.2)

v = 12.4 m/s

the speed of the car is 12.4 m/s

part C)

change in height , h = 0.11 * 54

h = 5.94 m

as the speed of car is constant

work done by friction = - M * h * g

work done by friction = -1369 * 9.8 * 5.94

work done by friction = - 79692 J

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