At the instant under consideration, the hydraulic cylinder AB has a length L = 0.75 m, and this length is momentarily increasing
at a constant rate of 0.2 m/s. If vA = 0.6 m/s and θ = 35°, determine the velocity of slider B.
2 answers:
Answer:
vB = - 0.176 m/s (↓-)
Explanation:
Given
(AB) = 0.75 m
(AB)' = 0.2 m/s
vA = 0.6 m/s
θ = 35°
vB = ?
We use the formulas
Sin θ = Sin 35° = (OA)/(AB) ⇒ (OA) = Sin 35°*(AB)
⇒ (OA) = Sin 35°*(0.75 m) = 0.43 m
Cos θ = Cos 35° = (OB)/(AB) ⇒ (OB) = Cos 35°*(AB)
⇒ (OB) = Cos 35°*(0.75 m) = 0.614 m
We apply Pythagoras' theorem as follows
(AB)² = (OA)² + (OB)²
We derive the equation
2*(AB)*(AB)' = 2*(OA)*vA + 2*(OB)*vB
⇒ (AB)*(AB)' = (OA)*vA + (OB)*vB
⇒ vB = ((AB)*(AB)' - (OA)*vA) / (OB)
then we have
⇒ vB = ((0.75 m)*(0.2 m/s) - (0.43 m)*(0.6 m/s) / (0.614 m)
⇒ vB = - 0.176 m/s (↓-)
The pic can show the question.
You might be interested in
Answer:
option (c) is the correct answer which is zero acceleration.
Explanation:
It is given in the question that the velocity is constant.
Now,
the options are provided in relation to the acceleration.
We know,
acceleration is rate of change of velocity per unit time i.e
acceleration =
since, the change in velocity is given to be zero,
thus, dV/dt = 0
hence,
acceleration = 0
therefore, option (c) is the correct answer which is zero acceleration.