Final answer:
To find the speed of the pendulum at the lowest point, we can apply the conservation of mechanical energy, using the potential energy at the starting height to calculate the kinetic energy at the lowest point. By putting the known values into the expression derived from equating potential and kinetic energy, the velocity can be calculated.
Step-by-step explanation:
The question concerns physics, specifically related to a simple pendulum and the concept of energy conservation. The student is asking how fast a pendulum with a mass of 1.5 kg, starting from a height of 0.4 m, is moving when it reaches the lowest point of its swing.
To determine the speed at the lowest point, we can use the principle of conservation of mechanical energy, which states that the sum of potential and kinetic energy in an isolated system remains constant if only conservative forces are acting. At the highest point, all energy is gravitational potential energy (assuming it starts from rest), and at the lowest point, all energy is kinetic. The potential energy at the height of 0.4 m is given by PE = m*g*h, where m is mass, g is acceleration due to gravity (9.81 m/s2), and h is the height. Kinetic energy at the lowest point is KE = 0.5*m*v2, where v is the velocity we need to find.
The equation for energy conservation will be m*g*h = 0.5*m*v2. Solving for v, we have v = sqrt(2*g*h). Substituting the known values, v = sqrt(2*9.81 m/s2*0.4 m), which gives us the speed at the lowest point.