# Mechanics forces acting on a object in a slope

• Nov 4th 2012, 06:25 PM
abdulrehmanshah
Mechanics forces acting on a object in a slope
Attachment 25548 answer to q15 is 2.42ms can anyone solve these questions please
• Nov 4th 2012, 06:38 PM
topsquark
Re: Mechanics forces acting on a object in a slope
Quote:

Originally Posted by abdulrehmanshah
Attachment 25548 answer to q15 is 2.42ms can anyone solve these questions please

Second, these are all Newton's 2nd Law problems. Can you show us how you set this up?

-Dan
• Nov 5th 2012, 07:12 AM
abdulrehmanshah
Re: Mechanics forces acting on a object in a slope
well can u please solve question 15 only once u solve it i will make change the topic to solved ok i copied it from a book
Quote:

Originally Posted by topsquark

Second, these are all Newton's 2nd Law problems. Can you show us how you set this up?

-Dan

• Nov 5th 2012, 08:06 AM
skeeter
Re: Mechanics forces acting on a object in a slope
forces acting on mass A ...

$\displaystyle T - Mg\sin{\theta} = Ma$

forces acting on mass B ...

$\displaystyle mg - T = ma$

combining equations ...

$\displaystyle mg - Mg\sin{\theta} = Ma + ma$

$\displaystyle \frac{m - M\sin{\theta}}{M + m} \cdot g = a$

this acceleration will be constant as mass A slides up 2.8 m ... use an appropriate kinematics equation to find the velocity of mass A when mass B hits the ground.

for the last 0.2 m, the only force acting on mass A will be the component of weight acting parallel to the incline, so mass A's acceleration will change ...

$\displaystyle g\sin{\theta} = a_2$

use the velocity found when mass B hits the ground, the acceleration $\displaystyle a_2$, and the remaining displacement to find the final velocity of mass A when it hits the pulley.
• Nov 5th 2012, 08:30 AM
abdulrehmanshah
Re: Mechanics forces acting on a object in a slope
this is where i got to but i cant get to the final velocity as 2.42ms^-1 can u please help me here
i write equation 2as=v^2-u^2.
2*4.9*0.2=v^2-u^2
what should be u(i.e initial velocity)
Quote:

Originally Posted by skeeter
forces acting on mass A ...

$\displaystyle T - Mg\sin{\theta} = Ma$

forces acting on mass B ...

$\displaystyle mg - T = ma$

combining equations ...

$\displaystyle mg - Mg\sin{\theta} = Ma + ma$

$\displaystyle \frac{m - M\sin{\theta}}{M + m} \cdot g = a$

this acceleration will be constant as mass A slides up 2.8 m ... use an appropriate kinematics equation to find the velocity of mass A when mass B hits the ground.

for the last 0.2 m, the only force acting on mass A will be the component of weight acting parallel to the incline, so mass A's acceleration will change ...

$\displaystyle g\sin{\theta} = a_2$

use the velocity found when mass B hits the ground, the acceleration $\displaystyle a_2$, and the remaining displacement to find the final velocity of mass A when it hits the pulley.

• Nov 5th 2012, 08:41 AM
ebaines
Re: Mechanics forces acting on a object in a slope
I suggest that you consider conservation of energy principles. There are two phases to this problem - the first phases is the 4 Kg mass being pulled up the ramp by the force of the 3Kg mass, and then the second phase is after the 3Kg mass hits the ground the tension in the rope becomes zero and the 4Kg mass continues to coast up uphill but slows as it rises. For phase 1 you have $\displaystyle \small\Delta KE + \Delta PE = 0$, where $\displaystyle \small \Delta KE = \frac 1 2 (m_A + M_B) v_1^2$ and $\displaystyle \small \Delta PE = m_A g (2.8m) \sin 30 = m_B g 2.8m$, so you can solve for $\displaystyle v_1$ . For phase 2: $\displaystyle \small \Delta KE = \frac 1 2 m_A (v_2^2-v_1^2) = m_A g (0.2m \sin 30)$
• Nov 5th 2012, 08:48 AM
abdulrehmanshah
Re: Mechanics forces acting on a object in a slope
what is the value of m
Quote:

Originally Posted by ebaines
I suggest that you consider conservation of energy principles. There are two phases to this problem - the first phases is the 4 Kg mass being pulled up the ramp by the force of the 3Kg mass, and then the second phase is after the 3Kg mass hits the ground the tension in the rope becomes zero and the 4Kg mass continues to coast up uphill but slows as it rises. For phase 1 you have $\displaystyle \small\Delta KE + \Delta PE = 0$, where $\displaystyle \small \Delta KE = \frac 1 2 (m_A + M_B) v_1^2$ and $\displaystyle \small \Delta PE = m_A g (2.8m) \sin 30 = m_B g 2.8m$, so you can solve for $\displaystyle v_1$ . For phase 2: $\displaystyle \small \Delta KE = \frac 1 2 m_A (v_2^2-v_1^2) = m_A g (0.2m \sin 30)$

• Nov 5th 2012, 09:12 AM
abdulrehmanshah
Re: Mechanics forces acting on a object in a slope
K.E=0.5*m*V where V is final velocity what have u done with phase 2
Quote:

Originally Posted by ebaines
I suggest that you consider conservation of energy principles. There are two phases to this problem - the first phases is the 4 Kg mass being pulled up the ramp by the force of the 3Kg mass, and then the second phase is after the 3Kg mass hits the ground the tension in the rope becomes zero and the 4Kg mass continues to coast up uphill but slows as it rises. For phase 1 you have $\displaystyle \small\Delta KE + \Delta PE = 0$, where $\displaystyle \small \Delta KE = \frac 1 2 (m_A + M_B) v_1^2$ and $\displaystyle \small \Delta PE = m_A g (2.8m) \sin 30 = m_B g 2.8m$, so you can solve for $\displaystyle v_1$ . For phase 2: $\displaystyle \small \Delta KE = \frac 1 2 m_A (v_2^2-v_1^2) = m_A g (0.2m \sin 30)$

• Nov 5th 2012, 09:58 AM
ebaines
Re: Mechanics forces acting on a object in a slope
"m" stands for "mass." You are told that the mass of block A is 4 Kg and the mass of block B is 3 Kg.

The change in kinetic energy of an object is: $\displaystyle \frac 1 2 mv_2^2 - \frac 1 2 mv_1^2$.
• Nov 5th 2012, 01:02 PM
skeeter
Re: Mechanics forces acting on a object in a slope
for the initial motion 2.8 m up the incline ...

$\displaystyle v_f^2 = v_0^2 + 2a(\Delta x)$

$\displaystyle v_f = \sqrt{2a(\Delta x)} = \sqrt{\frac{2g(2.8)}{7}} = \, 2.8 m/s$

for the final 0.2 m up the incline ...

$\displaystyle v_f^2 = 2.8^2 - g(0.2)$

$\displaystyle v_f = 2.42 \, m/s$
• Nov 5th 2012, 07:59 PM
abdulrehmanshah
Re: Mechanics forces acting on a object in a slope
how to change the topic to solved