Mechanics quesiton. Skateboarder on ramp.

In summary, a skateboarder with a total mass of 70kg starts from rest at the top of a ramp with a length of 25m and an angle of 20 degrees to the horizontal. The skateboarder has a velocity of 12.2m/s at the bottom of the ramp. The average acceleration of the skateboarder on the ramp is calculated using v^2 = u^2 + 2as. The component of the skateboarder's weight that is parallel to the ramp is found using the equation sin21=686/x. The initial centripetal force on the skateboarder is calculated using F=mv^2/r and the maximum height achieved is found using 1
  • #1
milan.007
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0

Homework Statement


A skateboarder with total mass of 70kg starts from rest at the top of a ramp and accelerates down it. The ramp is 25m long and is at an angle of 20 degrees to the horizontal. The skateboarder has a velocity of 12.2m/s at the bottom of the ramp.


Calculate
i) the average acceleration of the skate boarder on the ramp.
ii) the component of the skateboarders weight that is parallel to the ramp.
iii) the force of riction acting on the skateborader on the ramp.

The skateboarder then maintains a speed of 10.5m/s until he enters a circular ramp of radius 10m.
What is the initail centripetal force on him?
What is his maximum height achieved?


Homework Equations





The Attempt at a Solution


I used v^2 = u^2 + 2as to get the acceleration
I i found his weight 686N and used sin21=686/x, to find the parallel component.
Then for friction i substituted the parelel component from his weight (i think this is wrong).

For the second part, i used F=mv^2/r to find the centripetal force.
Thn i used 1/2mv^2 = mgh to ind the height.

Can someone do it and tell me if i used the correct formulas and please write the answers i want to compare them.
 
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  • #2
You're on the right track, you got the first question right.
aaverage = vf²/2s (Since vi=0)

I lost you at how you found the parallel component, though, try making a free body diagram of the skateboarder, and breaking mg down into its parallel and orthogonal components, relative to the ramp, using the 20° slope.

For the third question, I would approach with caution. Look at your free body diagram and your answers for questions i and ii.
Hint:
This will come in handy here: ΣF = m*a

As for the second question, could you please define it a bit more clearly? Does the friction continue to act on him? Because if so, then this question requires an integral of the force of friction to solve (If I remember the solution correctly), and I doubt that's what the teacher's aiming for, judging by the other questions.

Assuming there's no friction though, then yes, your solution looks correct. :)
 
  • #3
k thanks
 

Related to Mechanics quesiton. Skateboarder on ramp.

1. How does the skateboarder on a ramp maintain their balance?

The skateboarder maintains their balance through a combination of their body movements and the laws of physics. By shifting their weight and making small adjustments with their feet, the skateboarder can control their center of mass and keep the board and their body in equilibrium.

2. What forces are acting on the skateboarder as they go down the ramp?

Several forces act on the skateboarder as they go down the ramp. These include the force of gravity pulling them towards the center of the Earth, the normal force from the ramp pushing back on the skateboard, and friction between the wheels and the ramp.

3. How does the shape and angle of the ramp affect the skateboarder's speed?

The shape and angle of the ramp can greatly impact the skateboarder's speed. A steeper ramp will result in a greater gravitational force pulling the skateboarder down, while a curved ramp can provide a smoother and faster ride. Additionally, the friction between the wheels and the ramp can also affect the speed.

4. What happens to the skateboarder's potential and kinetic energy as they go down the ramp?

As the skateboarder goes down the ramp, their potential energy (stored energy due to their position) decreases while their kinetic energy (energy of motion) increases. This is because the skateboarder's height decreases as they go down the ramp, resulting in a decrease in potential energy, while their speed increases, resulting in an increase in kinetic energy.

5. How does the skateboarder stop or slow down at the end of the ramp?

The skateboarder can stop or slow down at the end of the ramp by using friction. By pushing their foot against the ground or dragging their foot on the ramp, they can create a force that opposes their motion and brings them to a stop. Alternatively, they can also use their body weight and balance to gradually slow down as they come to the end of the ramp.

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