Question

A hammer of mass 1 kg falls freely from a height of 20 m. a. Calculate the KE of the hammer just before it touches the ground. b. Calculate the velocity of the hammer just before it touches the ground. c. Does the velocity of a hammer depend on the mass of the hammer​

Answer 1

$\color{red}\huge{\underline{\underline{GIVEN\dag}}}$

• $Mass \: of \: hammer=1kg$
• $height = 20m$

$\color{red}\huge{\underline{\underline{TO\:FIND\dag}}}$

• $kinetic \: energy(KE)$
• $velocity(v)$
• $does \: velocity \: depend \: on \: mass$

$\color{red}\huge{\underline{\underline{SOLUTION\dag}}}$

$b).$

We know that;

Mechanical Energy(K.E+P.E) initial is equal to Mechanical Energy final.

${ \color{blue} \boxed{KE_{i}+PE_{i}=KE_{f}+PE_{f}}}$

But;

Intially velocity is 0 and when the hammer is about to touch ground potential energy(PE) is 0.

$\frac{1}{2} m {v}^{2} + mgh = \frac{1}{2} m {v}^{2} + mgh$

$\implies \frac{1}{2} (1) {(0)}^{2} + (1)(10)(20) = \frac{1}{2} (1) {(v)}^{2} + 0$

$\implies 200 = \frac{ {v}^{2} }{2}$

$\implies {v}^{2} = 400$

${ \boxed{ \color{orange}\therefore v = 20m {s}^{ - 1} }}$

$a).$

We know that;

$\color{blue}{ \boxed{KE = \frac{1}{2} m {v}^{2} }}$

$\implies KE = \frac{1}{2} (1) {(20)}^{2}$

${ \boxed{ \color{orange}\therefore KE =200 \: joules }}$

$c).$

$Velocity(v)\:of\:hammer\:is\:independent\\of\:mass.$

HOPE THAT HELPS!!

(glad to know it was helpful)

Answer 2

Answer:

velocity=√2gh

=√2*10*2

=2√10 m/s

ke=1/2 m v*v

=1/2*1*40

=20 joules

no velocity does not depend on mass of body