Power needed to accelerate up incline

In summary, an expert summarizer of content calculated the resistance to motion at 40km/h to be 327.25 Newtons and the effort required to achieve 40km/h to be 475.25 N. The power required to achieve 40km/h is 2637.6 watts.
  • #1
ferswin
5
0

Homework Statement


a vehicle of mass 200kg accelerates from rest up to 40km/h in 15seconds up an incline of 1 in 8. The resistance to motion can be considered to be in two parts, the first being due to friction and constant at 50 N/tonne with the second part being due to air resistance and being equal to 0.02v2 + v Newtons, where v is in km/hr.
a) Calculate the resistance to motion at 40km/h
b) Calculate the effort required to achieve 40km/h
c) Calculate the power required

d) we are later asked as part of coursework to choose a electric motor size for vehicle


Homework Equations





The Attempt at a Solution



a)whilst traveling at constant velocity

Force of air resistance (N) = 0.02*40^2+40 = 72 N
Rolling resistance (N) = 50 * 0.2t = 10 N
Force of incline (N) = 200*9.81*1/8 = 245.25

total resistance to motion at 40km/h (N) = 72+10+245.25 (N) = 327.25 N

b) Effort required = total resistance to motion + ma

to find a

v = 40km/h = 11.1m/s
u = 0 m/s
t = 15 s
a = ? m/s^2

v = u + at
11.1 (m/s)= a (m/s^2)*15(s)
a = 0.74 m/s^2

effort required = E = 327.25 (N)+ (200(kg)*0.74(m/s^2))
E = 475.25 N

c)
to find work done we need distance travelled

s = ut + 0.5at^2
s = 0.5*0.74(m/s^2)*15^2(t)
s = 83.25 m

workdone = 475.25(N)*83.25(m) = 39564.6 joules

Power = workdone/time = 39865.6(j)/15(s) = 2637.6 j/s (watts)

Power (hp) = 2598.2 / 745.7 = 3.49 hp

the answer I obtained doesn't take into account the varing air resistance would i need to find an average and recalculate?

in terms of selecting a suitable size motor if i work out the power needed at 39.9km/h with a acceleration of 0.74m/s^2 the power needed is

power = (total resistance + ma)*v

power = (475.25(N)+0.74(m/s^2)*200(kg))*11.1(m/s)
power = 6918 j/s

power (hp) = 6918/754.7 = 9.28 hp

I'm a little confused as why the power required to reach 40km/h is so less than power needed at 39.9km/h with a acceleration 0.74m/s^s. have i done calc wrong? what size motor do i go for? please help.
 
Physics news on Phys.org
  • #2
Your solution to (a) is correct. However, for (b) is the resistance to motion going to be constant throughout the acceleration?
 
  • #3
hi, thanks, do I need to try and find an average for air resistance?
 
  • #4
ferswin said:
hi, thanks, do I need to try and find an average for air resistance?
The effort required is going to be a function of velocity. Tell me have you solved any first order differential equations before? If not, I may be sending you off on a wild goose chase.
 
  • #5
no haven't done any 'first order differential equations before' will this be hard? the main of the cousework was to select a suitable motor and battery supply.
 
  • #6
ferswin said:
no haven't done any 'first order differential equations before' will this be hard? the main of the cousework was to select a suitable motor and battery supply.
What's your level? Have you done any calculus previously?
 
  • #7
it is BEng degree level (UK), I have gone back into education after many years so I'm quite rusty. but i know we haven't covered any differentiating in this course yet.
 
  • #8
I think I've over-complicating things a little here anyway. What you've done for (b) looks okay to me. However, for (c) I believe that you're going to have to take into account the varying air resistance as you say. Note that for motion in one dimension we define the work done by a variable force thus;

[tex]W = \int^{x_1}_{x_0}F\cdot dx[/tex]
 
  • #9
thanks, i'll some research into this, see if i can sovle it now
 

1. How does the incline of a surface affect the power needed to accelerate?

The steeper the incline of a surface, the more power is needed to accelerate an object up that incline. This is because the force of gravity is acting against the motion of the object, making it more difficult to move upwards.

2. Is more power needed to accelerate up an incline compared to a flat surface?

Yes, more power is needed to accelerate up an incline compared to a flat surface. This is due to the added resistance from gravity pulling the object downwards.

3. How does the mass of an object affect the power needed to accelerate up an incline?

The more massive an object is, the more power is needed to accelerate it up an incline. This is because a greater force is required to overcome the object's inertia and move it up the incline.

4. Can the power needed to accelerate up an incline be calculated?

Yes, the power needed to accelerate up an incline can be calculated using the formula P = mgv, where P is power, m is mass, g is the acceleration due to gravity, and v is velocity. This formula takes into account both the incline of the surface and the mass of the object.

5. Is there a maximum incline where an object cannot be accelerated with a certain power?

Yes, there is a maximum incline where an object cannot be accelerated with a certain power. This is due to the force of gravity becoming too great to overcome, and the object will either slide down the incline or come to a stop.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
212
  • Introductory Physics Homework Help
Replies
4
Views
991
  • Introductory Physics Homework Help
Replies
20
Views
882
  • Introductory Physics Homework Help
Replies
18
Views
3K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
565
  • Introductory Physics Homework Help
Replies
7
Views
3K
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
854
Back
Top