Question about Dynamics- force, acceleration

[mms05]

Could someone please help me with this problem?

A cyclist, pedaling at 20 km per hour, climbs a 1 km high hill in a half hour. What average total force must she supply in order for her to make it on time? Assume that the mass of the cyclist plus cycle is 50 kg. Would this answer be accurate "in real life" or only with certain unrealistic assumptions?

 

[Hootenanny]

What are your thoughts so far?

 

[mms05]

Well, I've been staring at it for the past hour, and what I can't figure out is whether the biker is still going up the hill at the same rate, or if the road flattened out- does that even matter? I know that the speed is 20 km/hr, and since the biker got up a 1 km hill in half an hour, giving her a velocity of 2 km/hr-- am I even close?

 

[Hootenanny]

Well, I've been staring at it for the past hour, and what I can't figure out is whether the biker is still going up the hill at the same rate, or if the road flattened out- does that even matter? I know that the speed is 20 km/hr, and since the biker got up a 1 km hill in half an hour, giving her a velocity of 2 km/hr-- am I even close?

What is important here is that the cyclist is traveling with a constant speed. What does this constant speed suggests about all the forces acting on the cyclist? I would recommend drawing a diagram. I think you are a little off with your speed calculation, take another look at the question;

A cyclist, pedaling at 20 km per hour, climbs a 1 km high hill in a half hour. What average total force must she supply in order for her to make it on time? Assume that the mass of the cyclist plus cycle is 50 kg.

A 1 km high hill means that at the top of the hill the cyclist has climbed 1km vertically, you need to use the speed (constant at 20km/hr) to calculate the length of the hill, the hypotenuse of a triangle.

 

[mms05]

Since the speed of the cyclist is constant, the forces acting on her should all add up to zero. The length of the hill is 20 km? (I just used dimensional analysis). If the forces add up to zero since she is going at a constant speed, how do I know what force she has to apply to keep going up the hill?

 

[Hootenanny]

Since the speed of the cyclist is constant, the forces acting on her should all add up to zero. The length of the hill is 20 km? (I just used dimensional analysis).

You may want to recheck your distance, the cyclist is traveling at 20km/h and she climbs in the hill in half an hour

If the forces add up to zero since she is going at a constant speed, how do I know what force she has to apply to keep going up the hill?

This is why I suggested drawing a diagram, what forces are acting down the slope (I think we can treat the cyclist as a particle and the hill as smooth, thus ignoring drag and friction etc.)?

 

[mms05]

ok, so she traveled 10 km in half an hour? I'm getting confused because the question states that the hill is 1 km long.

The forces acting on the slope are the weight of the cyclist/bike, and the normal force that's pushing up perpendicular to the slope, right?

 

[Hawknc]

It actually states that the hill is 1km HIGH. Imagine this is a cross-section of one side of the hill:

|\
|-\
|--\
|___\

The vertical line is 1km, you've worked out that the cyclist traveled 10km (the hypotenuse as Hootenany said), so you can work out what angle the cyclist is traveling at, and from that what propelling force is needed to counteract any other forces and maintain a constant speed (i.e. a net zero force).