Question

A 35.0-g object connected to a spring with a force constant of 40.0 N/m oscillates with an amplitude of 6.00 cm on a frictionless, horizontal surface.

(a) Find the total energy of the system.
mJ

(b) Find the speed of the object when its position is 1.15 cm. (Let 0 cm be the position of equilibrium.)
m/s

(c) Find the kinetic energy when its position is 2.50 cm.
mJ

(d) Find the potential energy when its position is 2.50 cm.
mJ

Answer 1

Part A

the total energy of the system

As the energy is conserved then we calculate it when the object is passing through the point where it has its maximum velocity because here the energy from the spring is zero

where is given by

where is the angular frequency and A is the amplitude.

is determined as follows

now we calculate the maximum speed

now we calculate the total energy

Find the speed of the object when its position is 1.15 cm. (Let 0 cm be the position of equilibrium.)

first we will find the work invested in the block

where is zero

Where W is

Find the kinetic energy when its position is 2.50 cm.

using the following definition

and considering that is ceron in

where

Find the potential energy when its position is 2.50 cm.