Problem 5: A massless spring (with force constant k-185 N/m) connects a wall and

Question

Problem 5: A massless spring (with force constant k-185 N/m) connects a wall and a block of wood. The system is initially at rest, with the spring unstretched. The block has mass M = 53.1 g and is able to move without friction on a table. A gun is positioned to fire a bullet of mass m 9.6 g into the block along the spring axis. After the gun is fired, the bullet gets embedded in the block, and the spring is compressed a maximum distance d- 0.8/m. Otheexpertta.com Part (a) Find an equation for the speed of the bullet v, just before it hits the block, in terms of the variables given in the problem statement SchematicChoice kd2 Part (b) In meters per second, what is the speed of the bullet v before it enters the block? Numeric A numeric value is expected and not an expression Part (c) What is the frequency f(in Hz) of the resulting periodic motion of the block/bullet and spring system? Numeric A numeric value is expected and not an expression

Explanation / Answer

here,

a)

let the final speed after the collison be v'

using conservation of energy

0.5 * ( m + M) * v'^2 = 0.5 * k * d^2

v' = sqrt(k * d^2 /(m + M))

let the intial speed of bullet be v

using conservation of momentum for the collison

m * v = (m + M) * v'

m * v = sqrt(k * d^2 /(m + M)) * ( m + M)

v = (d/m) * sqrt( k * ( m + M))

b)

spring constant , K = 185 N/m

Mass of block , M = 0.0531 kg

mass of bullet , m = 0.0096 kg

d = 0.81 m

v = ( 0.81 /0.0096) * sqrt(185 * ( 0.0531 + 0.0096)) m/s

v = 287.4 m/s

c)

the frequency , f = 1/(2*pi) * sqrt(k/(m + m))

f = 1/(2*pi) * sqrt(185/(0.0531 + 0.0096))

f = 8.65 Hz

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---