Calculate the gravitational potential energy of a body of mass 40 kg at a vertical height of 10 m. ( g = 9.8 m/s2)

A light platform is suspended from the ceiling by a spring. A student with a mass of 90 kg climbs onto the platform. When it sto

Ilya [14]

Refer to the diagram shown.

When the student climbs onto the platform, the spring stretches by 0.82 m to reach the equilibrium position.
The mass of the student is m = 90 kg, so his weight is
mg = (90 kg)*(9.8 m/s²) = 882 N

By definition, the spring constant is
k = (882 N)/(0.82 m) = 1075.6 N/m

When the spring is stretched by x from the equilibrium position, the restoring force is
F = - k*x.

If damping is ignored, the equation of motion is
F = m * acceleration
or
$m \frac{d^{2}x}{dt^{2}} = -kx \\ \frac{d^{2}x}{dt^{2}} + \frac{k}{m} x = 0$

Define ω² = k/m = 11.751 => ω = 3.457.
Then the solution of the ODE is
x(t) = c₁ cos(ωt) + c₂ sin(ωt)

x'(t) = -c₁ω sin(ωwt) + c₂ω cos(ωt)
When t=0, x' =0, therefore c₂ = 0

The solution is of the form
x(t) = c₁ cos(ωt)
When t = 0, x = 0.32 m. Therefore c₁ = 0.32

The motion is
x(t) = 0.32 cos(3.457t)
The single amplitude is 0.32 m, and the double amplitude is 0.64 m.

Answer:
0.32 m (single amplitude), or
0.64 m (double amplitude)

6 0

2 years ago

) is it possible for one component of a vector to be zero, while the vector itself is not zero?

Natalka [10]

The least number of component of a vector quantity is two. These are the x-component and the y-component.

The resultant vector, or vector as we refer to it in this item, can be calculated through the equation,
RV = sqrt ((Vx)² + (Vy)²)

From the equation, it can be noted that if we let Vx equal to zero,
RV = Vy

Similarly, if we let Vy be equal to zero then,
RV = Vx

Thus, it is still possible for the vector to become nonzero even if one of its components is zero.

8 0

3 years ago

Which of these common substances is a heterogeneous mixture?

LenaWriter [7]

Answer:

(C) If the composition of a mixture appears uniform no matter where you sample it, is homogeneous; sand on a beach *IS HETEROGENEOUS* because when you look at it up close, you can identify different types of particles, such as sand, shells, and organic matter.

Explanation:

(A) Pure Water is a collection of solely H2O molecules therefore Pure Water is classified as a *Compound*.

(B) Table Salt is NOT a heterogeneous mixture because the particles of salt can't be separated, and it is a *Pure Substance*.

(D) Maple Syrup is a homogeneous mixture because the solutes are fully dissolved and not easily identified. In other words, Maple Syrup is uniform throughout.

-Hope this helps!

4 0

3 years ago

How do you convert mass to weight and visa versa

Darina [25.2K]

To change from mass to weight is Fw = 30 kg * 9.8 m/s^2 = 294 N. To change from weight to mass divide by gravity (9.8 m/s^2).

6 0

3 years ago

Read 2 more answers

A spring with force constant of 59 N/m is compressed by 1.3 cm in a hockey game machine. The compressed spring is used to accele

Furkat [3]

Answer:

The puck moves a vertical height of 2.6 cm before stopping

Explanation:

As the puck is accelerated by the spring, the kinetic energy of the puck equals the elastic potential energy of the spring.

So, 1/2mv² = 1/2kx² where m = mass of puck = 39.2 g = 0.0392 g, v = velocity of puck, k = spring constant = 59 N/m and x = compression of spring = 1.3 cm = 0.013 cm.

Now, since the puck has an initial velocity, v before it slides up the inclined surface, its loss in kinetic energy equals its gain in potential energy before it stops. So

1/2mv² = mgh where h = vertical height puck moves and g = acceleration due to gravity = 9.8 m/s².

Substituting the kinetic energy of the puck for the potential energy of the spring, we have

1/2kx² = mgh

h = kx²/2mg

= 59 N/m × (0.013 m)²/(0.0392 kg × 9.8 m/s²)

= 0.009971 Nm/0.38416 N

= 0.0259 m

= 2.59 cm

≅ 2.6 cm

So the puck moves a vertical height of 2.6 cm before stopping

3 0

3 years ago