You will find the distance the first sled travels up the incline using kinematics, but first you need to find the sled's acceleration. Use forces to find the acceleration, then kinematics to find the distance.
To find the acceleration of the first sled, draw a force diagram. The force due to gravity is Fg=m*g and it points down. Don't worry that you don't know m because if you do the algebra right the m's will cancel in the end. The normal force points upward on an angle, perpendicular to the incline. Since there is no friction and no pulling force or anything else, those are your only forces.
Now make a chart with forces perpendicular to the incline, parallel to the incline, and in the "?" (idk) direction. The normal force (N) is in the perpendicular direction. The force due to gravity Fg is in the "?" direction. Now draw your triangle and use trig to find the components of Fg in the directions parallel and perpendicular to the incline: parallel is Fgsinθ; perpendicular is Fgcosθ.
Now you can use Newton's 2nd law to sum the forces in the direction parallel to the incline. If you use the sliding-down-the-incline as the positive direction (because the sled will be accelerating down the incline) then you get ∑F=Fgsinθ=ma. Replace Fg with m*g and solve for "a" (notice that your mass "m" cancels). That gives you the sled's acceleration (it will be the acceleration for the 2nd sled for #6 too).
Finally, since you know the acceleration you can find the distance that the sled travels up the incline using kinematics. Watch out for "-" signs. The sled has an initial positive velocity up the incline, and its final velocity is zero. Since it is slowing down its acceleration (that you just calculated) must be negative - don't forget the negative on the acceleration!
Thank you for explaining this Dr. Winters but once I find the acceleration, and I need to do the distance formula, how would I be able to find the distance if I dont have a number for time? Do I need to do a seperate equation to find time?
OK, so you have the acceleration. The problem gives you the initial velocity, and you know the final velocity is 0 since the sled comes to rest. There are a couple of ways to find the distance, and both use kinematics equations. You could use a separate equation to find the time and then use the distance equation to find the distance. Or you could use an equation that doesn't use time at all, but you would have to do some algebra to solve for the distance. Either way works. Good luck.
3 comments:
For #5 you only need to think about the 1st sled.
You will find the distance the first sled travels up the incline using kinematics, but first you need to find the sled's acceleration. Use forces to find the acceleration, then kinematics to find the distance.
To find the acceleration of the first sled, draw a force diagram. The force due to gravity is Fg=m*g and it points down. Don't worry that you don't know m because if you do the algebra right the m's will cancel in the end. The normal force points upward on an angle, perpendicular to the incline. Since there is no friction and no pulling force or anything else, those are your only forces.
Now make a chart with forces perpendicular to the incline, parallel to the incline, and in the "?" (idk) direction. The normal force (N) is in the perpendicular direction. The force due to gravity Fg is in the "?" direction. Now draw your triangle and use trig to find the components of Fg in the directions parallel and perpendicular to the incline: parallel is Fgsinθ; perpendicular is Fgcosθ.
Now you can use Newton's 2nd law to sum the forces in the direction parallel to the incline. If you use the sliding-down-the-incline as the positive direction (because the sled will be accelerating down the incline) then you get ∑F=Fgsinθ=ma. Replace Fg with m*g and solve for "a" (notice that your mass "m" cancels). That gives you the sled's acceleration (it will be the acceleration for the 2nd sled for #6 too).
Finally, since you know the acceleration you can find the distance that the sled travels up the incline using kinematics. Watch out for "-" signs. The sled has an initial positive velocity up the incline, and its final velocity is zero. Since it is slowing down its acceleration (that you just calculated) must be negative - don't forget the negative on the acceleration!
Hope that helps. Good luck.
Thank you for explaining this Dr. Winters but once I find the acceleration, and I need to do the distance formula, how would I be able to find the distance if I dont have a number for time? Do I need to do a seperate equation to find time?
OK, so you have the acceleration. The problem gives you the initial velocity, and you know the final velocity is 0 since the sled comes to rest. There are a couple of ways to find the distance, and both use kinematics equations. You could use a separate equation to find the time and then use the distance equation to find the distance. Or you could use an equation that doesn't use time at all, but you would have to do some algebra to solve for the distance. Either way works.
Good luck.
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