For the single slider crank mechanism shown in figure 1, the crank OBhas a constant clockwise angular velocity of 2000 rpm. For the crankposition indicated, determine (a) the angular velocity of the connectingrod BD, and (b) the velocity of the piston P (c) the angular accelerationof the connecting rod BD and the acceleration of point D (The Piston)

A vertical single cylinder engine has a cylinder diameter of 250 mm and stroke length of 450 mm. The reciprocating parts have a mass of 180 kg. The connecting rod is four times the crank radius and the speed is 360 r.p.m. when the crank has turned through an angle of 45° from top dead centre, the net pressure on the piston is 1.05 MN/m². Calculate the effective turning moment on the crankshaft for this position.

To solve this problem, we need to determine the velocity of the collar at \( A \) and the angular velocity of \( AB \). Given that the crank \( BC \) rotates with a constant angular velocity of \( \omega_{BC} = 6 \, \text{rad/s} \), we can use the principles of rotational kinematics and relative velocity. ### Step 1: Determine the velocity of point \( B \) The velocity of point \( B \) due to the rotation of crank \( BC \) can be found using the formula: \[ v_B = \omega_{BC} \times r_{BC} \] where \( r_{BC} \) is the length of the crank \( BC \). Given: \[ \omega_{BC} = 6 \, \text{rad/s} \] \[ r_{BC} = 1 \, \text{m} \] So, \[ v_B = 6 \, \text{rad/s} \times 1 \, \text{m} = 6 \, \text{m/s} \] ### Step 2: Determine the direction of \( v_B \) Since \( BC \) rotates in the \( xy \)-plane, the velocity \( v_B \) will be perpendicular to \( BC \). Given the configuration, \( v_B \) will be in the negative \( y \)-direction. ### Step 3: Determine the velocity of collar \( A \) The velocity of collar \( A \) can be found using the relative velocity equation: \[ \vec{v}_A = \vec{v}_B + \vec{\omega}_{AB} \times \vec{r}_{A/B} \] Since \( A \) and \( B \) are connected by the rod \( AB \), and \( AB \) is perpendicular to the angular velocity vector \( \omega_{AB} \), we can write: \[ \vec{v}_A = \vec{v}_B + \vec{\omega}_{AB} \times \vec{r}_{A/B} \] Given: \[ \vec{v}_B = -6 \, \hat{j} \, \text{m/s} \] \[ \vec{r}_{A/B} = 3 \, \hat{k} - 5 \, \hat{j} \, \text{m} \] Assuming \( \vec{\omega}_{AB} = \omega_{AB} \, \hat{i} \), we get: \[ \vec{\omega}_{AB} \times \vec{r}_{A/B} = \omega_{AB} \, \hat{i} \times (3 \, \hat{k} - 5 \, \hat{j}) \] \[ = \omega_{AB} (5 \, \hat{k} + 3 \, \hat{j}) \] So, \[ \vec{v}_A = -6 \, \hat{j} + \omega_{AB} (5 \, \hat{k} + 3 \, \hat{j}) \] Since \( A \) is constrained to move vertically along the \( z \)-axis, the \( \hat{j} \) component of \( \vec{v}_A \) must be zero: \[ -6 + 3 \omega_{AB} = 0 \] \[ \omega_{AB} = 2 \, \text{rad/s} \] ### Step 4: Calculate the velocity of collar \( A \) Now, substituting \( \omega_{AB} \) back into the equation for \( \vec{v}_A \): \[ \vec{v}_A = -6 \, \hat{j} + 2 (5 \, \hat{k} + 3 \, \hat{j}) \] \[ \vec{v}_A = -6 \, \hat{j} + 10 \, \hat{k} + 6 \, \hat{j} \] \[ \vec{v}_A = 10 \, \hat{k} \, \text{m/s} \] So, the velocity of the collar at \( A \) is \( 10 \, \text{m/s} \) in the \( z \)-direction, and the angular velocity of \( AB \) is \( 2 \, \text{rad/s} \).

The crankshaft is connected to what bearing

How many degrees of crankshaft rotation does the two stroke engine take to complete: intake, compression, power and exhaust strokes?*1 pointb) 720a) 180c) 360d) 90

What component on an engine changes the reciprocating motion of the pistons into rotary motion?*1 pointd) Flywheela) Connecting rodc) Camshaftb) Crankshaft