A 27.0 kg child on a 3.00 m long swing is released from rest when the swing supports make an angle of 31.0° with the vertical. Neglecting friction, find the child's speed at the lowest position.
mass is irrelevant for pendulum, cancels
Figure out how high the child is above the low point when the chains are 31 deg from vertical
h = 3 (1 - cos 31)
U at top = m g h
Ke at bottom = U at to
(1/2) m v^2 = m g h
v = sqrt (2 g h)
thanks!
If the speed of the child at the lowest position is 2.50 m/s, what is the mechanical energy lost due to friction?
mechanical energy lost= PE at top-1/2 m vb^2 where vb is the speed at the bottom
To find the child's speed at the lowest position, we can use the principle of conservation of mechanical energy. At the highest point, where the child is released, the swing possesses only potential energy, and at the lowest point, all of the potential energy is converted to kinetic energy.
The potential energy at the highest point can be calculated using the formula:
PE = m * g * h
where m is the mass of the child, g is the acceleration due to gravity (9.8 m/s^2), and h is the height at the highest point above the lowest position. Since the swing supports make an angle of 31.0° with the vertical, we can calculate the height as follows:
h = 3.00 m * sin(31.0°)
Next, we equate the initial potential energy to the final kinetic energy at the lowest point:
PE = KE
Since kinetic energy is given by:
KE = (1/2) * m * v^2
where v is the velocity of the child at the lowest point, we can solve for v by rearranging the equation:
v = sqrt((2 * PE) / m)
Substituting the values of PE and m, we can calculate v using calculator.
Note: Neglecting friction assumes that no external forces act on the swing, such as air resistance or friction at the pivot point.
I hope this explanation helps you understand how to solve this problem!