I tired and get the answer of 1.95 mm/s^2. However it is not correct. Can someon
ID: 1818213 • Letter: I
Question
I tired and get the answer of 1.95 mm/s^2. However it is not correct.
Can someone help me with this? Really stuck here. Thx a millllllllllllllllllllion!
Here's the question. A pin is constrained to move in a circular slot of radius 64mm. At the same time a slotted bar also constrains the pin to move down with a constant velocity of 4mm/s as shown. What is the magnitude of the acceleration of the pin for the postion shown? I tired and get the answer of 1.95 mm/s^2. However it is not correct. Can someone help me with this? Really stuck here. Thx a millllllllllllllllllllion!Explanation / Answer
1. The time it takes for the pin to move to the position shown is:
(64mm)*sin69o/(4mm/s)=14.9373s
2. The position of the pin can be expressed as follows:
x = 64 - 642-16t2 , y = -4t
the pin is moving downward in a costant acceleration, therefor we know that the magnitude of the acceleration of the pin comes from the sideways movement, namely x-direction movement.
Therefore,
we can re-write the equation as: x2 - 2*64*x = - 16t2
and, taking the differantial, we get: 2x*(dx/dt) - 2*64*(dx/dt) = -32t
taking the differantial again, we get: 2(dx/dt)+2x*(d2x/dt2) -2*64*(d2x/dt2)= -32
3. Substituding the time t we have caculated in 1., we get the position x. From t and x we can obtain the vlocity (dx/dt). And finally, the acceleration (d2x/dt2).