Physics, 01.11.2019 01:31 jacksonsmith0

Atoy cannon uses a spring to project a 5.38-g soft rubber ball. the spring is originally compressed by 5.08 cm and has a force constant of 7.91 n/m. when the cannon is fired, the ball moves 14.5 cm through the horizontal barrel of the cannon, and the barrel exerts a constant friction force of 0.032 3 n on the ball. (a) with what speed does the projectile leave the barrel of the cannon? m/s (b) at what point does the ball have maximum speed? cm (from its original position) (c) what is this maximum speed? m/s

Answers: 1

Show answers

Answers

Answer from: Lujfl

(a) 1.43 m/s

We can solve this problem by using the law of conservation of energy.

The initial total energy stored in the spring-mass system is

$E=U=\frac{1}{2}kx^2$

where

k = 7.91 N/m is the spring constant

x=5.08 cm = 0.0508 m

Substituting,

$E=\frac{1}{2}(7.91)(0.0508)^2=0.0102 J$

The final kinetic energy of the ball is equal to the energy released by the spring + the work done by friction:

E+W_f=K

where

$K_f=\frac{1}{2}mv^2$ is the kinetic energy of the ball, with

$m=5.38 g = 5.38\cdot 10^{-3} kg$ being the mass of the ball

v being the final speed

W_f = -F_f d is the work done by friction (which is negative since the force of friction is opposite to the motion), where

F_f = 0.0323 N is force of friction

d = 14.5 cm = 0.145 m is the displacement

Substituting,

$W_f = -(0.0323)(0.145)=-4.68\cdot 10^{-3} J$

So, the kinetic energy of the ball as it leaves the cannon is

$K_f = E+W_f = 0.0102 - 4.68\cdot 10^{-3}=0.00552 J$

And so the final speed is

$v=\sqrt{\frac{2K_f}{m}}=\sqrt{\frac{2(0.00552)}{0.00538}}=1.43 m/s$

(b) +5.08 cm

The speed of the ball is maximum at the instant when all the elastic potential energy stored in the spring has been released: in fact, after that moment, the spring does no longer release any more energy, so the kinetic energy of the ball from that moment will start to decrease, due to the effect of the work done by friction.

The elastic potential energy of the spring is

$U=\frac{1}{2}kx^2$

And this has all been released when it becomes zero, so when x = 0 (equilibrium position of the spring). However, the spring was initially compressed by 5.08 cm, so the ball has maximum speed when

x = +5.08 cm

with respect to the initial point.

The maximum speed is the speed of the ball at the moment when the kinetic energy is maximum, i.e. when all the elastic potential energy has been released.

As we calculated in part (a), the total energy released by the spring is

E = 0.0102 J

The work done by friction here is just the work done to cover the distance of

d = 5.08 cm = 0.0508 m

Therefore

$W_f = -(0.0323)(0.0508)=-1.64\cdot 10^{-3} J$

So, the kinetic energy of the ball at the point of maximum speed is

$K_f = E+W_f = 0.0102 - 1.64\cdot 10^{-3}=0.00856 J$

And so the final speed is

$v=\sqrt{\frac{2K_f}{m}}=\sqrt{\frac{2(0.00856)}{0.00538}}=1.78 m/s$

Answer from: Quest

Hypothesis. why don’t you know this? i learned this stuff in like 5th grade

Answer from: Quest

Ibelieve the answer you're looking for is

Another question on Physics

Physics, 21.06.2019 22:20

Acave rescue team lifts an injured spelunker directly upward and out of a sinkhole by means of a motor-driven cable. the lift is performed in three stages, each requiring a vertical distance of 11.0 m: (a) the initially stationary spelunker is accelerated to a speed of 4.80 m/s; (b) he is then lifted at the constant speed of 4.80 m/s; (c) finally he is decelerated to zero speed. how much work is done on the 78.0 kg rescue by the force lifting him during each stage

Answers: 2

Answer

Physics, 22.06.2019 14:30

Which compound is held together by the electrostatic force between two ions? a. co2 b. cci4 c. h2s d. mgf2

Answers: 1

Answer

Physics, 22.06.2019 15:30

The radius of a sphere is increasing at a rate of 9 cm/ sec. find the radius of the sphere when the volume and the radius of the sphere are increasing at the same numerical rate.

Answers: 1

Answer

Physics, 22.06.2019 19:00

Abatter hits a 0.140-kg baseball that was approaching him at 30 m/s and, as a result, the ball leaves the bat at 40 m/s in the reverse of its original direction. the ball remains in contact with the bat for 2.0 ms. what is the magnitude of the average force exerted by the bat on the ball?

Answers: 1

Answer

You know the right answer?

Atoy cannon uses a spring to project a 5.38-g soft rubber ball. the spring is originally compressed...

Questions