Question

It takes a force of 91.0 N to compress the spring of a toy popgun 0.175 m to ""load"" a 0.160-kg ball. With what speed will the ball leave the gun if fired horizontally?

a) 15.5 m/s
b) 20.7 m/s
c) 24.6 m/s
d) 30.2 m/s

Answer 1

The speed at which the ball will leave the gun when fired horizontally is 20.7 m/s.

Step-by-step explanation:

To find the speed at which the ball will leave the gun when fired horizontally, we can use the principle of conservation of mechanical energy. When the spring is compressed, it stores potential energy. When the ball is fired, this potential energy is converted into kinetic energy. By equating these two forms of energy, we can find the speed of the ball.

The potential energy stored in the spring is given by the equation:
PE = (1/2)kx^2
Where PE is the potential energy, k is the force constant of the spring, and x is the compression of the spring.

The kinetic energy of the ball is given by the equation:
KE = (1/2)mv^2
Where KE is the kinetic energy, m is the mass of the ball, and v is the velocity of the ball.

Setting the potential energy equal to the kinetic energy and solving for v, we get:

v = √((2kx^2) / m)

Plugging in the values given in the question, we have:
v = √((2 * 91.0 N/m * 0.175 m^2) / 0.160 kg) = 20.7 m/s