a 1300 kg car starts from rest at A , coasts 170m through a dip and comes to stop at B after coasting a distance d on level ground . if the rolling resistance is a constant force of 220N , determine the distance d .
Since there is no kinetic energy change from start to finish and zero energy added by the coasting engine, the potential energy change equals the rolling resistance times the distance travelled. A figure is needed to show the length and depth of the "dip". Is there rolling resistance loss before the level portion?
170m length dip and dips down 12m at the very bottom and up 5m to level ground. Distance =?
Kinetic energy gained passing through dip = M*g*(12-5) - 170*220
= 89180 - 37400
= 51,780 J
This is converted to rolling friction work after the dip
51,780 = 220*d
d = 235 m
To determine the distance d, we need to consider the work done by the rolling resistance and the work done by gravitational potential energy.
First, let's calculate the work done by the rolling resistance.
Work (W) = Force (F) x Distance (d)
In this case, the rolling resistance force (F) is given as 220N, and we need to find the distance d.
W = 220N x d
Next, we need to calculate the work done by the gravitational potential energy.
The change in gravitational potential energy is given by:
ΔPE = mgh
Where m is the mass of the car (1300 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height difference between points A and B. Since the height difference is not provided, we can assume it to be zero.
ΔPE = 1300 kg x 9.8 m/s^2 x 0 = 0 J
The work done by the gravitational potential energy is equal to the negative of the work done against the rolling resistance:
W = -ΔPE
Since W is zero, we can conclude that the work done against the rolling resistance is also zero.
So, we have:
220N x d = 0
d = 0 / 220N
d = 0 meters
Therefore, the distance d on level ground is 0 meters.