Question

The mine skip is being hauled to the surface over the curved track by the cable wound around the 20-in. drum, which turns at the constant clockwise speed of 93 rev/min. The shape of the track is designed so that y = x2/35, where x and y are in feet. Calculate the magnitude of the total acceleration of the skip as it reaches a level of 2.7 ft below the top.

Answer 1

To calculate the magnitude of the total acceleration of the skip as it reaches a level of 2.7 ft below the top, you can use the equations for x-component and y-component of acceleration. Substitute the values of x and y at that level and find the corresponding components. Finally, calculate the magnitude of the total acceleration using the formula a^2 = ax^2 + ay^2.

Step-by-step explanation:

To calculate the magnitude of the total acceleration of the skip as it reaches a level of 2.7 ft below the top, we need to determine the components of acceleration in the x and y directions. The x-component of acceleration is given by ax = -x(2/35) * (d^2x/dt^2), where x is the position of the skip along the track. The y-component of acceleration is given by ay = 2y(2/35) * (dy/dt)^2. At the level 2.7 ft below the top, we can substitute the values of x and y into these equations to find the corresponding values of ax and ay. Finally, the magnitude of the total acceleration (a) is given by a^2 = ax^2 + ay^2.