How Does the Work-Energy Principle Determine the Motion of a Thrown Rock?

[shakejuhn]

Homework Statement

You throw a 25.0N rock into the air from ground level and observe that, when it is 13.0m high, it is traveling upward at 21.0m/s

A. Use the work-energy principle to find the rock's speed just as it left the ground.

B. Use the work-energy principle to find the maximum height the rock will reach.

Homework Equations

=K.E.i+P.E.i=K.E.f+P.E.f
=.5(m)(vf)^2
=M*g*H

The Attempt at a Solution

so far i got
.5(25*9.8)(21.0)^2 + 0 = 31213
i know this is not rigth how do i use the equations to get the answers

 

[hage567]

Initially, the rock only has kinetic energy. When it is at 13 meters above the ground, it has both gravitational potential energy and kinetic energy. So you will have three terms to use in your conservation of energy equation.

Note: weight = m*g, so if you want to convert Newtons into kg it would be m = w/g, you seem to have it wrong in your work.

 

[ogb p]

The work-energy principle states that the total work done on an object is equal to the change in its kinetic energy and potential energy. In this case, the work done on the rock is due to the force of gravity, which is acting against the upward motion of the rock.

A. To find the rock's speed just as it left the ground, we can use the equation for kinetic energy: KE = 1/2mv^2. Since the rock's initial kinetic energy is zero (it is at rest on the ground), we can set up the equation as follows:

Work done by gravity = Change in kinetic energy
Mgh = 1/2mv^2
25*9.8*13 = 1/2*25*v^2
v = √(25*9.8*13*2/25) = 19.4 m/s

Therefore, the rock's speed just as it left the ground was 19.4 m/s.

B. To find the maximum height the rock will reach, we can use the equation for potential energy: PE = mgh. At its maximum height, the rock's kinetic energy is zero, so we can set up the equation as follows:

Work done by gravity = Change in potential energy
Mgh = mgh
25*9.8*h = 0 - 25*9.8*13
h = 13 m

Therefore, the maximum height the rock will reach is 13 m.