Conservation Of Energy With Friction

[cheese_whizz]

Homework Statement

Hi, I am having trouble with this problem. I'ld be very grateful if anyone could help me :) I've only done it with the conservation of energy way because I am not too sure how to go about it with the D'alembert principle.

A Car with a mass of 100kg is pulled along a horizontal surface by a force of 1000N. The car is initially at rest, and is pulled 25 meters. The co-efficient of friction between the car and road is 0.6.

Determine the acceleration of the car using the principle of conservation of energy and D’alemberts principle.

Car Mass: 100kg
Co-efficient of friction is 0.6
N = (mg) = 100 x 9.81 = 981N
Frictional Resistance (Fr) = μN = 0.6x981 = 588.6N
Distance = 25 meters.

The Attempt at a Solution

Using Conservation of energy:

PE + KE + Win = PE + KE + Wout + Losses
0 + 0 + (F x Distance) = 0 + (1/2 mv^2)+ 0 + (Fr x distance)

(F x Distance) - (Fr x distance) = 1/2 x mv^2

(1000N x 25meters) – (588.6 x 25 meters) = 1/2 x 1000v^2

(1000N x 25meters) – (588.6 x 25 meters) / (1/2 x 1000) = v^2

47.07 = v^2

6.86 m/s = V

Acceleration is 6.86 m/s

Any help would be much appreciated :)

 

[Doc Al]

6.86 m/s = V

Acceleration is 6.86 m/s

V is the final velocity, not the acceleration. You'll have to use some kinematics to get the acceleration from the velocity and the distance. (Or just apply Newton's 2nd law.)

 

[cheese_whizz]

hi,

Thanks for taking the time to respond.

I've used this equation before but the lecturer never told me it was kinematics :/

is everything correct now?

thanks again.

 

[Doc Al]

hi,

Thanks for taking the time to respond.

I've used this equation before but the lecturer never told me it was kinematics :/

is everything correct now?

The kinematic approach is fine, but I see that you made an error in calculating V² in your first post. Revisit that.

 

[cheese_whizz]

hmm, i did make a mistake

:/

Im getting 4.114 as acceleration now which seems correct

M x a = F
100 x 4.114 = 411.4N

Force - resistive force = F
1000N – 588.6 = 411.4N

So i think I got there :)

Would this be correct for the D'alembert principle method?

Thanks again :)

 

[Doc Al]

You got it!

 

[cheese_whizz]

excellent :) Thanks again for all your help