A20.0 kg wood ball hangs from a 1.30 m -long wire. the maximum tension the wire can withstand without breaking is 600 n . a 0.900 kg projectile traveling horizontally hits and embeds itself in the wood ball. what is the largest speed this projectile can have without causing the cable to break?

original work:

m = 20 kg wood ball + .9 kg projectile = 20.9 kg
ft max = 600 n
1.3 m radius

f = mar = ft - fg
m(v^2)/r = ft - fg

v = sqrt((r(ft - fg))/m)
v = sqrt((1.3m(600n - (20.9 kg)(9./20.9 kg)
v = 4.96 m/s

The largest speed the projectile can have without causing the cable to break is 115 m/s.

The given parameters;

Apply the principle of conservation of linear momentum;

The net force of the wood-projectile system in the circular path is calculated as follows;

The largest speed the projectile can have;

Thus, the largest speed the projectile can have without causing the cable to break is 115 m/s.

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115 m/s

Explanation:

Momentum before = momentum after

mu = (M + m) v

u = (M + m) v / m

u = (20.0 + 0.900) v / (0.900)

u = 23.2 v

Sum of the forces in the radial direction:

∑F = ma

T − (M + m) g = (M + m) v² / r

600 − (20.0 + 0.900) (9.8) = (20.0 + 0.900) v² / 1.30

v = 4.96

u = 23.2 (4.96)

u = 115 m/s

You correctly found the speed of the ball/projectile after the collision.  You just have to use conservation of momentum to find the projectile's speed before the collision.

im guessing the west of station b

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.