Respuesta :
Answer:
Explanation:
When a spring is compressed , potential energy is stored in it which is released later on to impart kinetic energy to the fired ball.
If a spring is compressed by x , energy stored in it is
1/2 k x² where k is spring constant , x is compression.
In this case
potential energy stored
= 1/2 x 8.08 x (4.99)² x 10⁻⁴
= 100.6 x 10⁻⁴ J
If v be the velocity of ball just after firing
Kinetic energy of ball = 1/2 m v²
= .5 x 5.28 x 10⁻³ x v²
= 2.64 x 10⁻ ³ v²
According to law of conservation of energy
energy stored in spring = kinetic energy of ball
100.6 x 10⁻⁴ = 2.64 x 10⁻³ v²
v² = 38.11 x 10⁻¹
v = 1.95 m /s
During travel through barrel , the velocity of ball is reduced due to work done by friction.
Work done by friction
Friction force x distance
.032 x 0.152 J
= 4.89 X 10⁻³ J
Loss of energy of ball
= 4.89 X 10⁻³ J
Net energy of the ball while coming out of barrel
= 100.6 x 10⁻⁴ - 4.89 X 10⁻³
= 10.06 x 10⁻³ - 4.89 x 10⁻³
= 5.17 x 10⁻³
If v₁ be the velocity of emergence of ball out of barrel
1/2 m v₁² = 5.17 x 10⁻³
.5 x 5.28 x 10⁻³ v₁² = 5.17 x 10⁻³
v₁² = .5106
v₁ = .7145 m/s
b ) The maximum speed will be at a point of time when spring un- compresses completely to impart velocity to the ball.
c ) The maximum speed will be equal to
1.95 m /s
