Answer to Question #246335 in Mechanical Engineering for Jew

Question #246335
A 10 kg ball falls form the height of 100 m (a) calculate the vertical speed of the ball during the first 4 seconds ,(b) calculate the height of the ball above the gorund during the first 4 seconds ,(c) calculate the kinetic and potential energies of the ball.(d) determine the total mechanical energy of the ball?
1
Expert's answer
2021-10-05T13:37:02-0400

Let positive y-axis be pointing up. Then


"v(t)=v_0-gt=-gt, v_0=0"

"y(t)=y_0+v_0t-\\dfrac{gt^2}{2}=y_0-\\dfrac{gt^2}{2}, v_0=0, y_0=100\\ m"

(a)


"v(4)=-9.81\\ m\/s^2(4\\ s)=-39.24\\ m\/s"

(b)


"y(4)=100\\ m-\\dfrac{9.81\\ m\/s^2(4\\ s)^2}{2}=21.52\\ m"

(c)


"P=mgy"

"P|_{t=0}=10\\ kg(9.81\\ m\/s^2)(100\\ m)=9810\\ J"

"P|_{t=4}=10\\ kg(9.81\\ m\/s^2)(21.52\\ m)=2111.112\\ J"

"K=\\dfrac{mv^2}{2}"

"K|_{t=0}=0"

"K|_{t=4}=\\dfrac{10\\ kg(-39.24\\ m\/s)^2}{2}=7698.888\\ J"

(d)


"E=P+K=const"

"E=9810\\ J+0\\ J=9810\\ J"

"=2111.112\\ J+7698.888\\ J"

The total mechanical energy of the ball is 9810 J and is conserved during the motion.



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