A small ball hangs on a light string of length 0.5 m. It is pulled aside until the string makes 90° with the vertical and released from rest. Ignoring air resistance, find its speed v at the lowest point.
A small ball hangs on a light string of length 3 m. It is pulled aside until the string makes 70° with the vertical and released from rest. Ignoring air resistance, find its speed v at the lowest point.
A block slides from rest down a slope at 30° to the horizontal. The coefficient of kinetic friction is 0.1. Find its speed v after it has slid 7 m along the slope.
A 1000 kg car drives up a 4° slope at a constant 72 km/h. Air resistance and rolling resistance together amount to 800 N. Find the power P the wheels must deliver, in kW.
A spring of stiffness 3000 N/m at the bottom of a 15° slope is compressed by 5 cm against a 1 kg block and released. The coefficient of kinetic friction between block and slope is 0.25. How far d up the slope does the block travel from the release point before it stops? (Ignore the short distance over which the spring pushes, i.e. take friction and gravity over the whole distance d.)
A spring of stiffness 800 N/m at the bottom of a 30° slope is compressed by 15 cm against a 2 kg block and released. The coefficient of kinetic friction between block and slope is 0.15. How far d up the slope does the block travel from the release point before it stops? (Ignore the short distance over which the spring pushes, i.e. take friction and gravity over the whole distance d.)
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