In an arcade game a 0.142 kg disk is shot across a frictionless horizontal surface by compressing it against a spring and releasing it. If the spring has a spring constant of 174 N/m and is compressed from its equilibrium position by 8 cm, find the speed with which the disk slides across the surface. Answer in units of m/s

Henry's equation d = at^2

is not correct, but there may be a compensating error somewhere else, such as in assuming constant acceleration. I get the same answer, however.

I prefer to use conservation of energy.

Stored spring potential energy
= kinetic energy when released

(1/2) k d^2 = (1/2) m V^2
V = d sqrt (k/m) = 0.08*sqrt(174/0.142)
= 2.8 m/s

Well, well, well! Looks like we have a springy situation here, don't we? So, we have a disk being shot out from a spring. Let's spring into action and solve this puzzle!

To find the speed of the disk, we'll need to use some good old physics. The potential energy stored in the spring is given by the formula:

PE = (1/2)kx^2,

where PE is the potential energy, k is the spring constant, and x is the displacement of the spring.

Now, we know that the potential energy stored in the spring converts into kinetic energy as the disk moves across the surface. The kinetic energy can be calculated using the formula:

KE = (1/2)mv^2,

where m is the mass of the disk and v is its velocity.

Since energy is conserved, we can equate the potential energy to the kinetic energy:

(1/2)kx^2 = (1/2)mv^2.

Let's plug in the values we have:
k = 174 N/m,
x = 0.08 m (since the spring is compressed by 8 cm),
m = 0.142 kg.

Now, let's fence in that equation and solve for v:

(1/2)(174 N/m)(0.08 m)^2 = (1/2)(0.142 kg)v^2.

Simplify that equation and solve for v, dear puzzler! Go ahead and show that equation who's the boss!

(Note: Make sure you rearrange the equation properly and take the square root at the end to find the speed in m/s. Let's keep those units consistent!)

Once you've calculated the answer, come back and let me know. I'll be here, juggling for your amusement!

To find the speed with which the disk slides across the surface, we can use the principle of conservation of mechanical energy. The compressed spring stores potential energy, which is converted into kinetic energy as the disk slides across the surface.

First, let's find the potential energy stored in the spring when it is compressed. The potential energy stored in a spring can be calculated using the formula:

Potential Energy = (1/2) * k * x^2

Where:
k is the spring constant (174 N/m)
x is the compression in meters (8 cm = 0.08 m)

Potential Energy = (1/2) * 174 N/m * (0.08 m)^2
Potential Energy = 0.5576 J

Now, the potential energy stored in the spring is converted into kinetic energy when the disk slides across the surface. The kinetic energy can be calculated using the formula:

Kinetic Energy = (1/2) * mass * velocity^2

Where:
mass is the mass of the disk (0.142 kg)
velocity is the speed with which the disk slides across the surface (which we want to find)

Since the potential energy is converted into kinetic energy, we can equate the two:

Potential Energy = Kinetic Energy

0.5576 J = (1/2) * 0.142 kg * velocity^2

Simplifying the equation:

0.5576 J = 0.071 J * velocity^2

Dividing both sides by 0.071 J:

velocity^2 = 0.5576 J / 0.071 J

velocity^2 = 7.861

Taking the square root of both sides:

velocity ≈ √7.861

velocity ≈ 2.803 m/s

Therefore, the speed with which the disk slides across the surface is approximately 2.803 m/s.

its is 1

Fs = 174 N/m * 0.08 m = 13.92 N. = Force of the spring.

a = Fs/m = 13.92 / 0.142 = 98 m/s^2. =
acceleration of the arcade game.

d = at^2 = 0.08 m.
98t^2 = 0.08,
t^2 = 0.000816,
t = 0.02857 s.

V = at = 98 * 0.02857 = 2.8 m/s.