The pendulum shown right has a mass of 0.26 kg and moves to the right from point B to point A. At point B the speed of the mass is 3.2 m/s.
(i) What is the change in the gravitational potential energy in the motion from B to A?
(ii) What is the mass speed at point A?
(iii) If the mass is increased to larger than 0.26kg, will the speed at point A INCREASE, DECREASE, or STAY THE
SAME?
To solve this problem, we need to understand the concepts of gravitational potential energy and conservation of mechanical energy.
(i) The change in gravitational potential energy is given by the equation:
∆PE = mgh
where:
∆PE is the change in gravitational potential energy,
m is the mass of the object (0.26 kg in this case),
g is the acceleration due to gravity (approximately 9.8 m/s^2),
and h is the change in height between point B and point A.
However, the vertical height change is not given in the problem statement. Without this information, we cannot calculate the change in gravitational potential energy.
(ii) The mass speed at point A can be determined using the principle of conservation of mechanical energy. According to this principle, the total mechanical energy (sum of kinetic energy and potential energy) is conserved in the absence of non-conservative forces like friction or air resistance.
At point B, the object has kinetic energy but no potential energy. Therefore, the total mechanical energy at point B is equal to the kinetic energy:
KE_B = (1/2)mv^2
where:
KE_B is the kinetic energy at point B,
m is the mass of the object (0.26 kg in this case),
and v is the speed at point B (given as 3.2 m/s).
At point A, the object has potential energy but no kinetic energy. Therefore, the total mechanical energy at point A is equal to the potential energy:
PE_A = mgh
where:
PE_A is the potential energy at point A,
m is the mass of the object (0.26 kg in this case),
g is the acceleration due to gravity (approximately 9.8 m/s^2),
and h is the height at point A.
Since the total mechanical energy is conserved, we can equate the kinetic energy at point B to the potential energy at point A:
(1/2)mv^2 = mgh
Solving for v:
v = sqrt(2gh)
(iii) If the mass is increased to larger than 0.26 kg, the speed at point A will stay the same. This is because the speed at point A depends on the acceleration due to gravity (g) and the height (h), but not on the mass of the object. As long as the height and gravitational acceleration remain the same, the speed at point A will not be affected by the change in mass.