How can I solve these two physics problems involving work and springs?

AI Thread Summary
The discussion revolves around solving two physics problems related to work and springs. The first problem involves calculating the minimum work needed to push a 950-kg car up a 9-degree incline, with considerations for friction. The second problem focuses on a trampoline artist's jump, requiring the calculation of his landing speed and how far he depresses the trampoline, modeled as a spring. Participants suggest using free body diagrams and Newton's second law to approach the incline problem, while also discussing energy conservation principles for the trampoline scenario. Overall, the thread emphasizes the need for proper application of physics formulas and concepts to solve these problems effectively.
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Any Hints??

I'm stuck on these 2 problems.. Any hints would be helpful!

1. What is the minimum work needed to push a 950-kg car 810m up along a 9 degree incline? a) ignore friction, b) assume the effective coefficient of a friction retarding the car is .25.

This is what I did, but I don't think it's correct... :
A) W= Fdcost = mdcost = (950)(810cos9) = 7.6 * 10^5 J.
B) Wfr= Ffr*x*cos(180+9) = .25 * 810 *cos189 = -200 J

2. A 65 kg trampoline artist jumps vertically upward from the top of a platform with a speed of 5 m/s. A) how fast is he going as he lands o nteh trampoline, 3 m below? b) if the trampoline behaves liek a sprign with spring stiffness constant 6.2 * 10 ^4 N/m how far does he depress it?
I got the a) part using .5mv^2 + mgy1 = .5mv^2 + mgy2
and found v= 9.15 m/s
b) I'm not sure which equation to use... I tried using .5mvi^2 + .5kx1^2 = .5mvf^2 + .5kx2^2 But I wasn't quite sure what to plug in, and when I tried all the different possibilities I did not get the corect answer.
 
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Nobody? Please help! I have a quiz this friday! I really need to know how to do these problems!
 
Fused do a Free body diagram for the body on the incline.
 
I did that, but I don't know how to put the information into formulas

Cyclovenom said:
Fused do a Free body diagram for the body on the i

ncline.
 
Use Newton's 2nd Law

\sum^{n}_{i=1} \vec{F}_{i} = m \vec{a}
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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