During a physic lab, the student ask to add waterto a 2 kg bucket conect by negl

Question

During a physic lab, the student ask to add waterto a 2 kg bucket conect by negligible mass rope to an 80kg car which each position on a track which inclined 15 degree above the horizontal.

a) Draw the free body diagram and write the Newton Second Law equation for each body, car and bucket.

b) Without considered friction what mass of water would be needed to start the car moving up?

c) Considering the friction coefficient between the car and the track equal to .200 and aditional 14.00 kg of water is added to the bucket how long will it take the car to move 34 m up to the track?

d) What is the weight of a 50 kg mass object measure in an elevator traveling upward at constant acceleration of 5 m/s^2 ?. How much the weight change if it is measured in the same elevatore moving with the same acceleration but downward?

Explanation / Answer

Ignoring friction, forces acting on

1. Car: Weight=Mg downwards and T along the track, upwards, T-Mgsin15=Ma

Bucket: weight=mg downwards and T in the rope upwards, mg-T= ma

2. Since the motions are constrained, hence acceleration of both the bodies is same.

For just moving the car , we can assume acceleration to be zero.

mg=Mgsin 15

m= 80 sin 15

m=20.7, so mass of water= 18.7kg

3. Now, for the car,

T-Mgsin 15-0.2Mgcos 15=Ma

mg-T=ma

From this, you get the value of a(acceleration)

Use, the equation, s=0.5at^2

where s=34 and you can find time taken

4.This weight measured is nothing but the normal reaction,

upward: N-mg= ma

N= 50(9.8+5)=740N

downward: mg-N=ma

N=50(9.8-5)=240N

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