A spring-loaded toy gun is used to shoot a ball of mass m =1.50kg straight up in

Question

A spring-loaded toy gun is used to shoot a ball of mass m=1.50kg straight up in the air, as shown in(Figure 1) . The spring has spring constant k=667N/m. If the spring is compressed a distance of 25.0 centimeters from its equilibrium position y=0and then released, the ball reaches a maximum heighthmax (measured from the equilibrium position of the spring). There is no air resistance, and the ball never touches the inside of the gun. Assume that all movement occurs in a straight line up and down along the y axis.

Find the maximum height hmax of the ball.

Explanation / Answer

Spring is compressed by x = 0.25 m
Spring potential energy at this point = 0.5*k*x^2
At this point let ggravitational potential energy is 0
Then at hmax, gravitational potential energy = m*g*(hmax + 0.25 )

At hmax, spring potential energy has converted into gravitational potential energy
so,
0.5*k*x^2 = m*g*(hmax + 0.25 )
0.5*667*(0.25)^2 = 1.5*9.8*(hmax + 0.25 )
(hmax + 0.25 ) =1.42
hmax = 1.17 m
Answer: 1.17 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.