Question

A pendulum is raised to a certain height and released from point A, as shown in the image below. At its release, the pendulum is also given an initial velocity of 14 m/s. Assuming that the effects of friction and air resistance can be ignored, what will be the maximum height that the pendulum can reach - that is , what is the height at point B? (Recall that g = 9.8 m/s2.)

Answer 1

D. 20 m

Explanation:

The potential energy at Point B will be the sum of the potential and kinetic energies at point A.

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energy formulas

For mass M, the potential energy at h meters above a rest height is ...

PE = Mgh

The kinetic energy of mass M with velocity v is ...

KE = 1/2Mv²

point A energy

A pendulum with mass M launched downward at v = 14 m/s will have a total energy of ...

PE +KE = M(9.8 m/s²)(10 m) +1/2(M)(14 m/s)² = M(98 +98) = 196M J/kg

point B energy

When the pendulum comes to rest at point B, its energy will all have been converted to potential energy. Then the height at point B is given by ...

PE = Mgh

196M J/kg = M(9.8 m/s²)h

h = (196M)/(9.8M) m = 20 m

The height of the mass at point B will be 20 meters.