Question

An 81.9 g mass is attached to a horizontal spring with a spring constant of 3.5 N/m and released from rest with an amplitude of 39.1 cm. What is the speed of the mass when it is halfway to the equilibrium position if the surface is frictionless? Answer in units of m/s.

Answer #1

When it is released with this energy it gains speed.

Half the amplitude is x/2.

At half the amplitude its p.e is 1/2 k [x/2]^2 = 1/8 kx^2.

Hence the remaining energy is converted into kinetic energy of the
mass m as 1/2 mv^2.

The remaining energy is 3/8 kx^2 = 1/2 mv^2

Substitute the values and find v.

3/8 *3.5* 0.391 ^2 = 1/2 *0.0819 v^2

v = - 2.21 m/s minus sign since it moves toward the equilibrium
position.

========================

A 0.58 kg mass is attached to a light spring with a force
constant of 31.9 N/m and set into oscillation on a horizontal
frictionless surface. If the spring is stretched 5.0 cm and
released from rest, determine the following.
(a) maximum speed of the oscillating mass
m/s
(b) speed of the oscillating mass when the spring is compressed 1.5
cm
m/s
(c) speed of the oscillating mass as it passes the point 1.5 cm
from the equilibrium position
m/s...

A 0.68 kg mass is attached to a light spring with a force
constant of 36.9 N/m and set into oscillation on a horizontal
frictionless surface. If the spring is stretched 5.0 cm and
released from rest, determine the following.
(a) maximum speed of the oscillating mass
m/s
(b) speed of the oscillating mass when the spring is compressed 1.5
cm
m/s
(c) speed of the oscillating mass as it passes the point 1.5 cm
from the equilibrium...

A block of mass m = 0.53 kg attached to a spring with force
constant 119 N/m is free to move on a frictionless, horizontal
surface as in the figure below. The block is released from rest
after the spring is stretched a distance A = 0.13 m. (Indicate the
direction with the sign of your answer. Assume that the positive
direction is to the right.)
The left end of a horizontal spring is attached to a vertical
wall, and...

. A block of mass 2.00 kg is attached to a horizontal spring
with a force constant of 500 N/m. The spring is stretched 5.00 cm
from its equilibrium position and released from rest. Use
conservation of mechanical energy to determine the speed of the
block as it returns to equilibrium
(a) if the surface is frictionless
(b) if the coefficient of kinetic friction between the block and
the surface is 0.350

A block with mass 0.382 kg is attached to a horizontal spring
with spring constant k = 1.28 N/m on a frictionless surface. The
block is pulled 0.753 m from equilibrium and released. (a) What is
the amplitude of the block's motion? (b) What is its period? (c)
How long after release does the block take to first return to its
equilibrium position? (d) What is its speed at that position? {b.
3.43 s, d. 1.38 m/s}
a) A=0.753m
b)...

A horizontal spring attached to a wall has a force constant of
760 N/m. A block of mass 1.30 kg is attached to the spring and
oscillates freely on a horizontal, frictionless surface as in the
figure below. The initial goal of this problem is to find the
velocity at the equilibrium point after the block is released.
(c) Find the energy stored in the spring when the mass is
stretched 5.80 cm from equilibrium and again when the mass...

A student stretches a spring, attaches a 1.70 kg mass to it, and
releases the mass from rest on a frictionless surface. The
resulting oscillation has a period of 0.530 s and an amplitude of
26.0 cm. Determine the oscillation frequency, the spring constant,
and the speed of the mass when it is halfway to the equilibrium
position.
(a) the oscillation frequency (in Hz)
Hz
(b) the spring constant (in N/m)
N/m
(c) the speed of the mass (in m/s)...

A horizontal spring attached to a wall has a force constant of
k = 820 N/m. A block of mass m = 1.20 kg is
attached to the spring and rests on a frictionless, horizontal
surface as in the figure below
(a) The block is pulled to a position xi =
5.40 cm from equilibrium and released. Find the potential energy
stored in the spring when the block is 5.40 cm from
equilibrium.
(b) Find the speed of the block...

A horizontal spring attached to a wall has a force constant of
k = 720 N/m. A block of mass m = 1.90 kg is
attached to the spring and rests on a frictionless, horizontal
surface as in the figure below.
(a) The block is pulled to a position xi = 6.20
cm from equilibrium and released. Find the potential energy stored
in the spring when the block is 6.20 cm from equilibrium.
(b) Find the speed of the block...

A 0.24 kg mass is attached to a light spring with a force
constant of 30.9 N/m and set into oscillation on a horizontal
frictionless surface. If the spring is stretched 5.0 cm and
released from rest, determine the following.
(a) maximum speed of the oscillating mass
b) speed of the oscillating mass when the spring is compressed
1.5 cm
(c) speed of the oscillating mass as it passes the point 1.5 cm
from the equilibrium position
(d) value of...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 15 minutes ago

asked 20 minutes ago

asked 23 minutes ago

asked 30 minutes ago

asked 44 minutes ago

asked 51 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago