General Physics Q: Find Acceleration, Velocity, Speed

[ken62310]

a general physics q please help!

A bob rotates clockwise in a vertical circle at the end of a 1 m long rope. In the pint, where the rope makes the horizontal to the right, the acceleration of the bob is (-2i+3j)m/s^2. At that instant
-sketch the acceleration vector and find its magnitude,
-find tangential and radial acceleration,
-find velocity and speed of the ball
-is the speed increasing or decreasing in this point?

 

[hage567]

Show us what you have done. Explain what you are confused about.

 

[m2003]

To find the acceleration, velocity, and speed of the bob, we can use the kinematic equations of circular motion. First, we can sketch the acceleration vector at the point where the rope makes the horizontal to the right. This vector will have a magnitude of √(4+9) = √13 m/s^2 and a direction of 45 degrees below the horizontal.

Next, we can find the tangential and radial acceleration using the formula a_t = v^2/r and a_r = v^2/r, where v is the velocity and r is the radius of the circle. Since the radius is 1 m, the tangential acceleration will be equal to v^2, and the radial acceleration will be equal to v^2/1 = v^2. Solving for v, we get v = √(a_t*r) = √(4*1) = 2 m/s. This is the velocity of the bob at the point where the rope makes the horizontal to the right.

To find the speed, we can use the formula v = ω*r, where ω is the angular velocity. Since the bob is rotating at a constant speed, we can assume that ω is constant. Therefore, the speed of the bob will be equal to the velocity, which is 2 m/s.

Since the acceleration vector is pointing in the opposite direction of the velocity vector, we can conclude that the speed is decreasing at this point. This means that the bob is slowing down as it moves along the circle.