Question

A block with mass m =7.5 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.25 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.1 m/s. The block oscillates on the spring without friction.

After t = 0.3 s what is the speed of the block?

What is the magnitude of the maximum acceleration of the block?

At t = 0.3 s what is the magnitude of the net force on the block?

Where is the potential energy of the system the greatest?

At the highest point of the oscillation.

At the new equilibrium position of the oscillation.

At the lowest point of the oscillation.

Answer #1

Now we can use the velocity equation

v(t) = - A w sin (wt - phi) [eq 1}

w = sqrt(k/m) = 5.48 rad/s

Hmmmml...to find A, I guess we have to us conservation of
energy,

(1/2) k x^2 = (1/2) m v^2

x^2 = v^2 * m/k

x = sqrt (v^2 * m / k)

x = A = 0.74814 m

Now plug everything into eq 1

v = - (0.7481) * (5.48rad/s) sin (5.48rad/s*0.3sec - pi/2)

v = 4.1m/s

4)

kA = ma,

a = kA/m

a = (294.3N/m) (0.7481/ 7.5kg)' . Kx=mg , k =mg/x

a = 29.4 m/s^2

5) the net force is the spring force at t = 0.3sec.

Fnet = k * x, so we just need x when t = 0.3sec.

x(t) = - A cos (wt - phi)

x = (0.7481m) cos (5.48rad/s*0.3sec - pi/2)

x = 0.62m

Fnet = k * x = 182.40 N

Potential energy will be highest at above equalibrium position.

A block with mass m =6.2 kg is hung from a vertical spring. When
the mass hangs in equilibrium, the spring stretches x = 0.22 m.
While at this equilibrium position, the mass is then given an
initial push downward at v = 4.6 m/s. The block oscillates on the
spring without friction.
What is the spring constant of the spring?
2)
What is the oscillation frequency?
After t = 0.32 s what is the speed of the block?
What...

A block with mass m =7.3 kg is hung from a vertical spring. When
the mass hangs in equilibrium, the spring stretches x = 0.29 m.
While at this equilibrium position, the mass is then given an
initial push downward at v = 5 m/s. The block oscillates on the
spring without friction.
1) What is the spring constant of the spring? N/m Submit
2) What is the oscillation frequency? Hz Submit
3) After t = 0.45 s what is...

A block with mass m =7.1 kg is hung from a vertical spring. When
the mass hangs in equilibrium, the spring stretches x = 0.24 m.
While at this equilibrium position, the mass is then given an
initial push downward at v = 4.5 m/s. The block oscillates on the
spring without friction.
1) What is the spring constant of the spring?
2) What is the oscillation frequency?
3) After t = 0.38 s what is the speed of the...

A block with mass m =6.7 kg is hung from a vertical spring. When
the mass hangs in equilibrium, the spring stretches x = 0.27 m.
While at this equilibrium position, the mass is then given an
initial push downward at v = 4.5 m/s. The block oscillates on the
spring without friction.
1. What is the spring constant of the spring?
2. What is the oscillation frequency?
3. After t = 0.46 s what is the speed of the...

When a 0.411 kg mass is hung from a certain spring it stretches
0.148 m to its equilibrium position at point P. If this mass is
pulled down 0.139 m from point P and released, what is the
magnitude of the velocity in m/s of this mass 0.041 m from point
P?

When a 0.427 kg mass is hung from a certain spring it stretches
0.122 m to its equilibrium position at point P. If this mass is
pulled down 0.151 m from point P and released, what is the
magnitude of the velocity in m/s of this mass 0.0392 m from point
P? A 1.42 m3 piece of wood with a density of 0.805 kg/m3 floats in
the ocean where the density of the water is 1.027 kg/m3. What is
the...

A block of mass m = 1.5 kg is attached to a massless,
frictionless vertical spring and stretches the spring by an amount
y0 = 0.15m
a)find the spring constant k of the spring
b) the block is then pulled down by an additional 0.05m below
its equilibrium position and is released. express the position of
the block during its resulting simple harmonic motion using the
equation y(t) = ymcos(wt+@).
c) find the maximum acceleration fo the block A(m).
d)...

a) A block with a mass of 0.600 kg is connected to a spring,
displaced in the positive direction a distance of 50.0 cm from
equilibrium, and released from rest at t = 0. The block then
oscillates without friction on a horizontal surface. After being
released, the first time the block is a distance of 15.0 cm from
equilibrium is at t = 0.200 s.
What is the block's period of oscillation?
_______ s
b) A block with a...

A block with a mass of 0.600 kg is connected to a spring,
displaced in the positive direction a distance of 50.0 cm from
equilibrium, and released from rest at t = 0. The block then
oscillates without friction on a horizontal surface. After being
released, the first time the block is a distance of 25.0 cm from
equilibrium is at t = 0.200 s.
a.What is the block's period of oscillation?
_______ s
b.What is the the numerical value...

A 4.00 kg block hangs from a spring, extending it 16.0 cm from
its unstretched position.
(a.) What is the spring constant? = 245 N/m
(b.) The block is removed, and a 0.500 kg mass is hung from the
same spring. If the spring is then stretched and released, what is
its period of oscillation? =.284 sec
(c.) Write the unique equation of motion y(t) for the motion of
the mass in part (b), assuming the mass was initially pulled...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 23 minutes ago

asked 23 minutes ago

asked 27 minutes ago

asked 29 minutes ago

asked 34 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago