A pendulum has 343 J of kinetic energy at the lowest point in its swing. At the highest point in its swing, it has a height of 5 m. What is the pendulum's mass?

To find the mass of the pendulum, we can use the principle of conservation of energy.

At the lowest point, the pendulum's kinetic energy is given as 343 J. The kinetic energy of an object is given by the equation:

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

where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.

Since the pendulum is at the lowest point, its velocity is at its maximum. Therefore, we can rewrite the equation as:

KE = (1/2) * m * (v_max)^2.

We can rearrange this equation to solve for the velocity squared:

(v_max)^2 = (2 * KE) / m.

Now, we need to find the velocity at the highest point. According to the conservation of energy, the potential energy at the highest point is equal to the total energy at the lowest point. The potential energy is given by:

PE = m * g * h,

where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height.

Since the potential energy at the highest point is equal to the total energy, we can write:

PE = KE + m * g * h.

Substituting the values given in the question, we get:

m * g * h = KE + m * g * h,

343 J = (1/2) * m * (v_max)^2 + m * g * 5 m.

Now, we can substitute the equation we derived earlier for (v_max)^2:

343 J = (1/2) * m * [(2 * KE) / m] + m * g * 5 m.

We can simplify this equation to solve for the mass:

343 J = KE + 10 * m * g.

Since we know the value of KE and g, we can now calculate the mass of the pendulum.

Let's substitute the values:

343 J = 343 J + 10 * m * 9.8 m/s^2.

Now, we can simplify the equation:

0 = 10 * m * 9.8 m/s^2.

Dividing both sides by 9.8 m/s^2:

0 = 10 * m.

Therefore, the mass of the pendulum is 0 kg.