Engineering Mechanics

Step 1: Understanding Coriolis acceleration.
Coriolis acceleration occurs when a particle moves relative to a rotating body.
Step 2: Formula for Coriolis acceleration.
The Coriolis component of acceleration is given by: where is angular velocity and is relative velocity.
Step 3: Applying the given values.
Since the slider has velocity on a link rotating at angular speed , the Coriolis acceleration becomes:
Step 4: Conclusion.
The Coriolis component of acceleration is .

Step 1: Resolving initial velocity.
The vertical component of initial velocity is:
Step 2: Using equation of motion.
At maximum height, final vertical velocity becomes zero. Using:
Step 3: Solving for maximum height.

Step 4: Conclusion.
The maximum height attained by the projectile is

Step 1: Definition of coefficient of restitution.
The coefficient of restitution is defined as the ratio of the relative velocity of separation to the relative velocity of approach along the line of impact.
Step 2: Writing the mathematical expression.
Before impact, relative velocity of approach: After impact, relative velocity of separation:
Step 3: Formula substitution.

Step 4: Conclusion.
The correct expression for the coefficient of restitution is

Step 1: Writing the formula for resultant of two forces.
If two forces of equal magnitude act at an angle , the magnitude of their resultant is given by:
Step 2: Applying the given condition.
It is given that the resultant has the same magnitude as either of the forces. Therefore: Substituting into the formula:
Step 3: Solving for the angle.
Squaring both sides and simplifying: This gives:
Step 4: Conclusion.
The angle between the two equal forces is .

Step 1: Writing expressions for tension.
Let the mass of the lift be and acceleration be .
When the lift moves upwards with acceleration : When the lift moves downwards with acceleration :
Step 2: Applying the given condition.
It is given that the downward tension is half the upward tension: Substituting values:
Step 3: Solving for acceleration.
Canceling and simplifying:
Step 4: Conclusion.
The acceleration of the lift is .