Frictionless pulley Question (1 Viewer)

[nsbrando]

Two blocks, P and Q, of mases 4kg and 8 kg respectively are connected by a light inetensible string and hung over a frictionless pulley as shown in the following diagram

a. If the two blocks are allowed to move freely, calculate the resultant accerlation of the 8kg mass

b. Calculate the tension force in the string at X

c If the bottom surfaces of the blocks were level before they were released, from rest, how far apart would these surfaces be 0.2s after the block started to move?

 

[someth1ng]

W=mg

W(8kg)=8(9.8)
W(8kg)=78.4N

W(4kg)=4(9.8)
W(4kg)=39.2N

F(net on 8kg)=78.4-39.2=39.2N
39.2=8a
a=4.9ms-2

 

[someth1ng]

I think T=(8+4)9.8

 

[D94]

You need two equations, one for P and another for Q.

Let's assign some values to variables:
T = Tension
m_Q = m₁ = 8 kg
m_P = m₂ = 4 kg
a = acceleration
g = gravity = 9.81 m/s²

At Q, let's say the mass is going to move downwards, we have a Tension going up the string (acting just above the block) and the weight force. So we can come up with an equation:

m₁g - T = m₁a.

i.e. the weight force is larger than tension, so it accelerates downwards.

At P, the block is moving upwards so that means the tension acting upwards is greater than the weight force, causing it to accelerate upwards.

T - m₂g = m₂a

Solving simultaneous equations, we get that:

a = g x (m₁-m₂)/(m₁+m₂) = 3.27 m/s² downwards

[HR][/HR]

Given a = 3.27, we sub this into the equation for P.

T - m₂g = m₂a

T = m₂a + m₂g = 52.32 N upwards

[HR][/HR]

And for the last part, it's a vertical projectile motion question:

y = (1/2)*a*t² = 327/5000 m

But that's only for one side, we need to double that to account for the system moving upwards and downwards, so y = 327/2500 m or 13.08cm.

NOTE: we should probably make clear on what the pos/neg directions are. In the first equation, I took pos as downwards, and in the second equation, I took pos as upwards. If my 'a' was negative then I know my assumed direction was wrong.

 

[soloooooo]

Is this first year uni physics?

 

[Rathaen]

If by first year physics you mean that you don't need to know it for HSC then no, but the lecturer might cover something similar very briefly in the first week, and then you'll learn other stuff that'll actually be in your finals.

 

[Mr Slick]

It is not HSC physics, it is more like MX2 question