Can you work out power without knowing displacement?

[jjones1573]

Homework Statement

I'm a bit confused by a question asking me to work out the power of a bike traveling up an inclined plane with a constant speed. I have the mass and friction and the speed but no displacement so I don't know how I could work out power if to find the work I need to factor in displacement to the equation. Any ideas?

Homework Equations

The Attempt at a Solution

 

[PhanthomJay]

Power is W/t, and work is F.d, thus P = F.(d/t).

 

[jhae2.718]

Power can be found in terms of force and velocity; iff both are constant: P = F ∙ v

 

[jjones1573]

Ah ok great!

 

[jjones1573]

So If the bike is moving up at a constant speed with a friction force of 320N, to calculate the net force do I simply do mg Sin theta - 700?

Also when working interms of km/h do we need to convert to m/s to do the calculations?

 

[cepheid]

So If the bike is moving up at a constant speed with a friction force of 320N, to calculate the net force do I simply do mg Sin theta - 700?

Also when working interms of km/h do we need to convert to m/s to do the calculations?

The speed is constant, so you know that the net force is zero. Therefore, whatever force is being applied by the cyclist is being countered by friction and by the component of the weight parallel to the incline. In other words, the sum of all forces acting parallel to the incline is 0. You can use this force balance equation to solve for what the cyclist's applied force has to be.

Draw a free body diagram for the bike if you're having trouble keeping track of the forces.

Yes, you have to convert to m/s IF you want your answer to be in watts (N*m / s). If you don't, then your answer will be in (N*km/h), which is still a unit of power, but is not the standard one (the watt).

 

[jjones1573]

Ah ok thank you. so if the sum of all the forces parallel equals zero then perpundicular forces also cancel each other out then the net force is 0? I am still a little confused.

 

[cepheid]

Yes exactly. Let's just use tilted coordinate axes so that parallel to the incline is the x direction and perpendicular is the y direction. Then the condition for equilibrium gives you two equations 1. Sum of all forces in x-direction = 0
2. Sum of all forces in y direction = 0.

These two equations allow you to solve for your unknowns (friction, normal force) in terms of your knowns (mass, g, friction coefficient).

 

[sona1177]

Homework Statement

I'm a bit confused by a question asking me to work out the power of a bike traveling up an inclined plane with a constant speed. I have the mass and friction and the speed but no displacement so I don't know how I could work out power if to find the work I need to factor in displacement to the equation. Any ideas?

Homework Equations

The Attempt at a Solution

Think about the definition of velocity. What is in the numerator?

 

[jjones1573]

v = d/t

ahh I see what your saying that's why P = F.(d/t) or P = F.V because V = d/t of course!


But I'm still confused about the force calculation. if the net force is 0 then the power from the above equation p = 0 * velocity = 0
but that can't be right?

 

[cepheid]

v = d/t

ahh I see what your saying that's why P = F.(d/t) or P = F.V because V = d/t of course!


But I'm still confused about the force calculation. if the net force is 0 then the power from the above equation p = 0 * velocity = 0
but that can't be right?

It's true that there is no net work being done, and hence no net power output. Any power generated by the cyclist is 1. dissipated as heat due to friction OR 2. used up to increase the gravitational potential energy of the bike as it goes up the incline.

But the question is not asking you to compute the net power output. It is asking you to compute the power output of the cyclist. So don't use the net force in P = F*v. Use the applied force of the cyclist.

That's why you have to go through this whole rigamarole of applying the condition for static equilibrium and force balance -- to determine what force the cyclist has to apply to keep the bike moving.

 

[jjones1573]

Ah ok thank you for taking the time to explain this that makes complete sense now!