Need help on part B!

A 2.50 mass is pushed against a horizontal spring of force constant 26.0 on a frictionless air table. The spring is attached to the tabletop, and the mass is not attached to the spring in any way. When the spring has been compressed enough to store 15.0 of potential energy in it, the mass is suddenly released from rest.
a. Find the greatest speed the mass reaches? (Answer: 3.46 m/s)
b. What is the greatest acceleration of the mass?

Sorry, it was an accident. Geesh. It didn't copy and paste correctly.

To find the greatest acceleration of the mass, we can use the principle of conservation of mechanical energy.

The potential energy stored in the spring is given by the formula:

PE_spring = (1/2) * k * x^2

Where:
PE_spring is the potential energy stored in the spring (given as 15.0 J)
k is the force constant of the spring (given as 26.0 N/m)
x is the displacement of the spring from its equilibrium position (unknown)

Rearranging the equation, we get:

x^2 = (2 * PE_spring) / k

Substituting the given values, we have:

x^2 = (2 * 15.0 J) / 26.0 N/m
x^2 = 0.5769
x ≈ 0.76 m (taking the positive square root)

Now, let's consider the conservation of energy:

Initially, the mass is at rest, so it has no kinetic energy (KE_initial = 0 J).
At the maximum speed, the mass will have the maximum kinetic energy (KE_max).
The total energy remains the same, so the sum of the initial potential energy (PE_initial) and the maximum kinetic energy (KE_max) will be equal to the potential energy stored in the spring (PE_spring).

PE_initial + KE_max = PE_spring

Since the mass is initially at rest, there is no initial kinetic energy (KE_initial = 0 J).

0 J + KE_max = 15.0 J

Solving for KE_max:

KE_max = 15.0 J

The kinetic energy is given by the formula:

KE = (1/2) * m * v^2

Where:
KE_max is the kinetic energy at maximum speed (given as 15.0 J)
m is the mass of the object (given as 2.50 kg)
v is the maximum speed (unknown)

Rearranging the equation, we get:

v^2 = (2 * KE_max) / m

Substituting the given values, we have:

v^2 = (2 * 15.0 J) / 2.50 kg
v^2 = 12.0
v ≈ 3.46 m/s (taking the positive square root)

Therefore, the greatest acceleration of the mass is not asked in part b. However, if you need it, you can calculate it by using Newton's second law of motion:

F_net = m * a

Where:
F_net is the net force on the mass (which is equal to the force exerted by the spring)
m is the mass of the object (given as 2.50 kg)
a is the acceleration (unknown)

The force exerted by the spring is given by Hooke's Law:

F_spring = -k * x

Where:
F_spring is the force exerted by the spring (known as 26.0 N)
k is the force constant of the spring (given as 26.0 N/m)
x is the displacement of the spring from its equilibrium position (0.76 m)

Substituting the given values, we have:

F_net = -k * x

m * a = -k * x

a = (-k * x) / m

Substituting the given values, we have:

a = (-26.0 N/m * 0.76 m) / 2.50 kg
a ≈ -7.90 m/s^2 (negative because it is restoring force)

Therefore, the greatest acceleration of the mass is approximately -7.90 m/s^2.

To find the greatest acceleration of the mass, we can use the conservation of mechanical energy. Initially, the spring is compressed and contains potential energy, which is then transferred to the kinetic energy of the mass as it is released.

Step 1: Determine the potential energy stored in the spring.
The potential energy stored in a spring is given by the equation:
PE = (1/2) * k * x^2

In this case, we are given that the spring stores 15.0 J of potential energy (PE), and the force constant (k) is 26.0 N/m. We need to solve for the displacement (x).

Rearranging the equation, we have:
15.0 J = (1/2) * 26.0 N/m * x^2

Step 2: Solve for x.
To find x, we can rearrange the equation:
x^2 = (2 * PE) / k

Substituting the given values:
x^2 = (2 * 15.0 J) / 26.0 N/m

Calculating:
x^2 = 0.5769
x ≈ 0.760 m

Step 3: Calculate the acceleration.
The acceleration of the mass can be determined using the equation for the force exerted by the spring:
F = k * x

Substituting the given values:
F = 26.0 N/m * 0.760 m

Calculating:
F ≈ 19.76 N

Now, using Newton's second law, F = m * a, we can solve for the acceleration (a).

Substituting the values:
19.76 N = 2.50 kg * a

Calculating:
a ≈ 7.904 m/s^2

Therefore, the greatest acceleration of the mass is approximately 7.904 m/s^2.

The greatest acceleration is w^2 times the maximum deflection.

w is the angular frequency, which equals k/m

You have not provided dimensions for you numbers, so that is all the help you are going to get.

Learn the importance of dimensions with the numbers you use in physics, or don't expect to pass the course.