There is a basic difference, because mass is the actual amount of material contained in a body and is measuredin kg, gm, etc. Whereas weight is the force exerted by the gravity on that object mg. Note that mass is independent of everything but weight is different on the earth
Answer:
a) x=63.0
or 6.3cm
b) x=116.0
or 11.6cm
Explanation:
a).
The elastic potential energy is modeling by equation :
![U1=\frac{1}{2}*k*x^{2} \\K=1600 \frac{N}{m}\\ U=3.2J\\m=1.2kg\\x^{2}=\frac{2*U}{k}\\x=\sqrt{\frac{2*3.2J}{1600 \frac{N}{m}}} \\x=\sqrt{4x10^{-3} m^{2}}\\ x=0.06324m](https://tex.z-dn.net/?f=U1%3D%5Cfrac%7B1%7D%7B2%7D%2Ak%2Ax%5E%7B2%7D%20%5C%5CK%3D1600%20%5Cfrac%7BN%7D%7Bm%7D%5C%5C%20U%3D3.2J%5C%5Cm%3D1.2kg%5C%5Cx%5E%7B2%7D%3D%5Cfrac%7B2%2AU%7D%7Bk%7D%5C%5Cx%3D%5Csqrt%7B%5Cfrac%7B2%2A3.2J%7D%7B1600%20%5Cfrac%7BN%7D%7Bm%7D%7D%7D%20%5C%5Cx%3D%5Csqrt%7B4x10%5E%7B-3%7D%20m%5E%7B2%7D%7D%5C%5C%20x%3D0.06324m)
b).
The work energy theorem explain which work is done in this case. the motion began from the rest so K1=K2 equal zero, Ug1 is no yet done and U2is also zero because is the potential energy
![Ug=K2\\mgy=\frac{1}{2}*k*x^{2} \\but \\y=h+x=0.80m+x\\m*g*(0.80m+x)=\frac{1}{2}*k*x^{2}](https://tex.z-dn.net/?f=Ug%3DK2%5C%5Cmgy%3D%5Cfrac%7B1%7D%7B2%7D%2Ak%2Ax%5E%7B2%7D%20%5C%5Cbut%20%5C%5Cy%3Dh%2Bx%3D0.80m%2Bx%5C%5Cm%2Ag%2A%280.80m%2Bx%29%3D%5Cfrac%7B1%7D%7B2%7D%2Ak%2Ax%5E%7B2%7D)
Solving for x
![2*(m*g(h+x))=k*x^{2} \\k*x^{2}-(2*m*g*x)-(2*m*g*h)=0\\1600x^{2} -2*1.2kg*9.8\frac{m}{s^{2}}*x-2*1.2kg*0.80m=0\\1600x^{2} -23.52x-18.816m=0](https://tex.z-dn.net/?f=2%2A%28m%2Ag%28h%2Bx%29%29%3Dk%2Ax%5E%7B2%7D%20%5C%5Ck%2Ax%5E%7B2%7D-%282%2Am%2Ag%2Ax%29-%282%2Am%2Ag%2Ah%29%3D0%5C%5C1600x%5E%7B2%7D%20-2%2A1.2kg%2A9.8%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%2Ax-2%2A1.2kg%2A0.80m%3D0%5C%5C1600x%5E%7B2%7D%20-23.52x-18.816m%3D0)
![x=-\frac{b+/-\sqrt{b^{2}-4*a*c } }{2*a} \\x=-\frac{-23.52+/-\sqrt{-23.52^{2}-4*1600*-18.816 } }{2*a} \\x=11.79 +/- 173.9\\x1=-0.10 m\\x2=0.116](https://tex.z-dn.net/?f=x%3D-%5Cfrac%7Bb%2B%2F-%5Csqrt%7Bb%5E%7B2%7D-4%2Aa%2Ac%20%7D%20%7D%7B2%2Aa%7D%20%5C%5Cx%3D-%5Cfrac%7B-23.52%2B%2F-%5Csqrt%7B-23.52%5E%7B2%7D-4%2A1600%2A-18.816%20%7D%20%7D%7B2%2Aa%7D%20%5C%5Cx%3D11.79%20%2B%2F-%20173.9%5C%5Cx1%3D-0.10%20m%5C%5Cx2%3D0.116)
The negative is discard so
x=0.116m
Answer:
d = 13.7 m
Explanation:
When block is moving upwards along the inclined plane
then the block is decelerated due to gravity as well as due to friction and speed of the block by which it is projected upwards is given
![v_i = 15 m/s](https://tex.z-dn.net/?f=v_i%20%3D%2015%20m%2Fs)
deceleration caused to the block due to net force opposite to the motion is given as
![F = - mg sin\theta - \mu mgcos\theta](https://tex.z-dn.net/?f=F%20%3D%20-%20mg%20sin%5Ctheta%20-%20%5Cmu%20mgcos%5Ctheta)
![a = \frac{F}{m}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7BF%7D%7Bm%7D)
![a = -g(sin\theta + \mu cos\theta)](https://tex.z-dn.net/?f=a%20%3D%20-g%28sin%5Ctheta%20%2B%20%5Cmu%20cos%5Ctheta%29)
since block is sliding on the inclined plane
so here we can say that the coefficient of the friction must be kinetic friction here
![a = -9.81(sin31.5 + 0.368 cos31.5)](https://tex.z-dn.net/?f=a%20%3D%20-9.81%28sin31.5%20%2B%200.368%20cos31.5%29)
![a = - 8.2 m/s^2](https://tex.z-dn.net/?f=a%20%3D%20-%208.2%20m%2Fs%5E2)
now for finding the distance upto which it will stop is given as
![v_f^2 - v_i^2 = 2 a d](https://tex.z-dn.net/?f=v_f%5E2%20-%20v_i%5E2%20%3D%202%20a%20d)
![0 - 15^2 = 2(-8.2) d](https://tex.z-dn.net/?f=0%20-%2015%5E2%20%3D%202%28-8.2%29%20d)
![d = 13.7 m](https://tex.z-dn.net/?f=d%20%3D%2013.7%20m)
Answer: The correct answer is "Number of rope segments supporting the load".
Explanation:
Mechanical advantage: It is defined as the ratio of the force produced by a machine to the force applied on the machine. The ideal mechanical advantage of a machines is mechanical advantage in the absence of friction.
The ideal mechanical advantage of a pulley system is equal to the number of rope segments which is supporting the load. More the rope segments, It is more helpful to do the lifting the work.
It means that less force is needed for this task to complete.
Therefore, the correct option is (C).