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2D Dynamics

With 2D dynamics, we can explain the orbit of the planets around the Sun, the grandfather clock, and the perfect angle to throw a snowball to nail your nemesis as they run away from you.

Centripetal Acceleration

         

A rock tied to a string is moving at a constant speed of \( 8.0 \text{ m/s} \) in a circle of radius \( 7.0 \text{ m}. \) Calculate the approximate magnitude of the centripetal acceleration of the rock.

The above picture is a \(1000\) kg car passing the top of a hill with radius of curvature \(250\) m at a speed of \(50\) m/s. Find the magnitude of normal force on the car (in N).

Gravitational acceleration is \(g= 10\) m/s\(^{2}\).

A puck of mass \( m = 1.80 \text{ kg} \) slides in a circle of radius \( r = 50.00 \text{ cm} \) on a frictionless table while attached to a hanging ball of mass \( M = 3.50 \text{ kg}\) by a cord through a hole in the table, as shown in the figure above. Approximately how fast must the puck move in order to keep the ball at rest?

The gravitational acceleration is \( g =10 \text{ m/s}^2. \)

A block is hung by a string from the roof of a van. The van drives along a straight, flat road at a constant speed of \( 15 \sqrt{2} \text{ m/s}, \) and the block hangs vertically down. Then the van goes around an unbanked curve of radius \( 45.0 \text{ m} \) while maintaining the same speed, and the string tilts by an angle of \( \theta .\) Find the value of \( \theta. \)

The gravitational acceleration is \( g= 10 \text{ m/s}^2. \)

A rock tied to a string is moving at a constant speed of \( 1.8 \text{ m/s}\) in a circle. If the rock's acceleration is \( 3.6 \text{ m/s}^2, \) what is the approximate radius of the circle it moves in?

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