A crane is used to swing a 450 kg wrecking ball into a 500 kg wall. The crane takes 5 s to push the ball into the building. The crane provides 2000 N of force. The ball is left moving 10 m/s after the collision. How fast is the wall moving afterwards? *
How does the kinetic energy change in the crane problem?
1. KE increases
2. KE decreases
3. KE stays the same
This is a momentum problem, so let's find the velocity of the ball initially. It can be given by: [tex]\vec{F} = m\vec{a}[/tex] Let's plug in values and solve for a: [tex]\vec{a} = \frac{2000}{450} = 4.44 m/s^2[/tex] Now, we can multiply by time to get velocity: [tex]\vec{v} = \vec{a}t = 4.44(5) = 22.2m/s[/tex]
We have all the information we need, so let's set up an equation to solve for the velocity of the wall after the collision: [tex]mv_{ib}= mv_{fb} + mv_{w}[/tex]
Solve for velocity of wall finally: [tex]v_w = \frac{mv_{ib}-mv_{fb}}{m} [/tex]
Plug in all values: [tex]v_w = \frac{450(22.2)-450(10)}{500} = 10.98 \frac{m}{s} [/tex]
So, the final velocity of the wall will be 10.98 m/s. The KE in this problem initially was 110889 J (1/2mv^2). After the collision it was 52640.1 so, the KE decreased. Since there was no mashing of objects together, this was an elastic collision.
