Conservation of Mechanical Energy
At a construction site, a 1.50-kg brick is dropped from rest and hits the ground at a speed of 26.0 m/s. Assuming air resistance can be ignored, calculate the gravitational potential energy of the brick before it was dropped.
Read and Understand
What information are you given?
Mass, m = 1.50 kg
Final speed, v = 26.0 m/s
What unknown are you trying to calculate?
Gravitational potential energy of the brick before it was dropped, PE
Plan and Solve
What equations or formulas contain the given quantities and the unknown?
Because the brick falls without air resistance, the conservation of mechanical energy equation can be used.
You will also need to use the formula for kinetic energy (KE).
Note that the KE at the beginning is zero because the brick has not yet begun to fall. Also, when the brick hits the ground, its potential energy is zero. Substitute these values into the conservation of energy formula.
Substitute the formula for KE.
Substitute the known values and calculate the PE.
Look Back and Check
Is your answer reasonable?
Check the answer by finding the initial height of the brick, using PE = 507 J = mgh. Substituting in m and g gives h = 34.5 m. This is a reasonable height for an object in free fall to reach a speed of 26.0 m/s.
A 10-kg rock is dropped and hits the ground below at a speed of 60 m/s. Calculate the gravitational potential energy of the rock before it was dropped. You can ignore the effects of friction.
A diver with a mass of 70.0 kg stands motionless at the top of a 3.0-m-high diving platform. Calculate his potential energy relative to the water surface while standing on the platform, and his speed when he enters the pool. (Hint: Assume the diver's initial vertical speed after diving is zero.)
A pendulum with a 1.0-kg weight is set in motion from a position 0.04 m above the lowest point on the path of the weight. What is the kinetic energy of the pendulum at the lowest point? (Hint: Assume there is no friction.)