A wrecking ball is swinging at just the right height so that the student can stand at the bottom of the trajectory (lowest point) and grab onto the ball to swing – something that is just way too tempting for this inquisitive student. In order to justify invading the construction zone, before the student jumps on she attaches a magnet to an accelerometer and sticks the accelerometer onto the iron ball. The maximum velocity reading before she jumps on is 1.98m/s. Once she is on the ball, she reads that the maximum speed of herself and the ball together is 1.90 m/s. What is the mass of the wrecking ball?

Question

A wrecking ball is swinging at just the right height so that the student can stand at the bottom of the trajectory (lowest point) and grab onto the ball to swing – something that is just way too tempting for this inquisitive student. In order to justify invading the construction zone, before the student jumps on she attaches a magnet to an accelerometer and sticks the accelerometer onto the iron ball. The maximum velocity reading before she jumps on is 1.98m/s. Once she is on the ball, she reads that the maximum speed of herself and the ball together is 1.90 m/s. What is the mass of the wrecking ball?

length of cable of wrecking ball is 13m

Answer 1

conservation of momentum:

initial=final
M*1.98=(M+m)1.90
and you are looking to solve for Mass wrecking ball, but it was not given the mass of the idiot student, m.

So....I guess I would do an estimate by making an estimate for the idiot student's mass, say, 60kg
with that
M/(M+60)=1.90/1.98
or
M=(1.90/1.98)(M+60)
M(.08)=(1.90*60/1.98)
and you can solve M IF m=60kg

Answer 2

To solve this problem, we can apply the principle of conservation of mechanical energy. At the lowest point of the trajectory, the wrecking ball has its maximum potential energy and minimum kinetic energy. When the student jumps onto the ball, the system gains kinetic energy, while at the same time, some energy is lost due to friction and air resistance.

Let's denote the mass of the wrecking ball as "m" and the combined mass of the student and the wrecking ball as "M" (where M = m + student's mass).

We know the initial velocity of the wrecking ball, v_initial = 1.98 m/s, and the final velocity of the combined system, v_final = 1.90 m/s.

The mechanical energy at the highest point of the trajectory is equal to the sum of the kinetic and potential energy:

E_initial = KE_initial + PE_initial
E_final = KE_final + PE_final

Since the initial and final potential energies are the same (at the highest point, PE_initial = PE_final = 0), we can write:

KE_initial = KE_final.

The kinetic energy of an object can be calculated as (1/2) * mass * velocity^2. Applying this formula, we get:

(1/2) * m * v_initial^2 = (1/2) * M * v_final^2.

From this equation, we can substitute M with m + student's mass:

(1/2) * m * v_initial^2 = (1/2) * (m + student's mass) * v_final^2.

Now we have an equation with one unknown, the mass of the wrecking ball (m). We can solve for it.

However, we also need the mass of the student in order to find the mass of the wrecking ball. Without that information, we cannot find the answer to the problem.