Plus the following three problems: A ball, mass 0.250kg, is placed in a spring-l

Question

Plus the following three problems: A ball, mass 0.250kg, is placed in a spring-loaded cannon. The cannon is set horizontally on a table, height of 1.2m off the floor. The spring is released, causing the ball to shoot off the table. The speed of the ball as it leaves the cannon is 7.07m/s. It lands on the floor, 3.50m away from the table. Define the height to be zero on the ground. Calculate the speed of the ball just before hitting the floor. IGNORE AIR DRAG. Calculate the kinetic energy just as it leaves the cannon, so at a speed of 7.07 m/s. Calculate the gravitational potential energy just as it leaves the cannon. (Again, the ground has a height of zero.) Calculate the Total energy just as it leaves the cannon. Calculate the kinetic energy just before it strikes the ground. Calculate the potential energy BEFORE it's shot out of the cannon. Include both the gravitational AND the spring potential energies.

Explanation / Answer

here ,

mass of ball, m = 0.25 kg

height , h = 1.2 m

a)

let the final speed of ball is v

Using third equation of motion

v^2 - u^2 = 2 * a * d

v^2 - 7.07^2 = 2 * 9.8 * 1.2

solving for v

v = 8.57 m/s

the speed of the ball before hitting the ground is 8.57 m/s

b)

kinetic energy = 0.5 * m * v^2

kinetic energy = 0.5 * 0.25 * 7.07^2

kinetic energy = 6.25 J

c)

gravitational potential energy = m *g * h

gravitational potential energy = 0.25 * 9.8 * 1.2

gravitational potential energy = 2.94 J

the gravitational potential energy is 2.94 J

d)
total energy = gravitational potential energy + 0.5 * m * v^2

total energy = 2.94 + 0.5 * 0.25 * 7.07^2

total energy = 9.19 J

the total energy is 9.19 J

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