Question

A 0.900 kg orament is hanging by a 1.50 m wire when the ornament is suddenly hit by a 0.300 kg missile traveling horizontally at 12.0 m/s. The missile embeds itself in the ornament during the collision. Part A What is the tension in the wire immediately after the collision? Express your answer with the appropriate units.

Answer 1

The tension in the wire immediately after the collision is 11.76 N.

Step-by-step explanation:

To determine the tension in the wire immediately after the collision, we can use the principle of conservation of momentum. Before the collision, the missile and the ornament have different velocities, so their momenta are not equal. However, after the collision, they combine and move together, so their total momentum is conserved.

Using the equation for conservation of momentum, we can write:

m1v1 + m2v2 = (m1 + m2)v

where m1 and m2 are the masses of the missile and the ornament respectively, v1 and v2 are their respective velocities before the collision, and v is their common velocity after the collision.

Substituting the given values:

(0.300 kg)(12.0 m/s) + (0.900 kg)(0 m/s) = (0.300 kg + 0.900 kg)v

Simplifying the equation gives:

v = 3.27 m/s

Since the wire is hanging vertically, the tension in the wire is equal to the weight of the ornament and the missile combined:

Tension = (mass of ornament + mass of missile) × g

Plugging in the values:

Tension = (0.900 kg + 0.300 kg)(9.8 m/s²)

Taking the sum:

Tension = 11.76 N

Answer 2

To find the tension in the wire immediately after a collision, we use conservation of momentum to calculate the new velocity and then apply Newton's second law to calculate the tension. The tension in the wire is the sum of the gravitational force and the centripetal force required for the new circular motion of the combined mass, which is approximately 18.96 N.

Step-by-step explanation:

The question is about determining the tension in the wire immediately after a collision in which a missile embeds itself in an ornament. To solve this problem, we use the principle of conservation of momentum to find the velocity of the combined mass just after the collision and then apply Newton's second law to determine the tension.

First, we find the combined mass's velocity using the conservation of momentum:

Initial momentum = (mass of missile × velocity of missile) + (mass of ornament × velocity of ornament)

Since the ornament is initially at rest, its velocity is 0 m/s:

Initial momentum = (0.300 kg × 12.0 m/s) + (0.900 kg × 0)

Initial momentum = 3.6 kg·m/s

After the collision, the combined mass moves as one body:

Final momentum = (combined mass) × (final velocity)

3.6 kg·m/s = (0.900 kg + 0.300 kg) × (final velocity)

Final velocity = 3.0 m/s

Now we calculate the tension in the wire. The only forces immediately after the collision are the tension in the wire and the gravitational force on the combined mass, so:

Tension = Gravitational force + Centripetal force required for circular motion

Tension = (combined mass × gravity) + (combined mass × (velocity)^2 / wire length)

Tension = ((0.900 kg + 0.300 kg) × 9.8 m/s²) + ((0.900 kg + 0.300 kg) × (3.0 m/s)^2 / 1.50 m)

Tension = (1.200 kg × 9.8 m/s²) + (1.200 kg × 9.0 m²/s² / 1.50 m)

Tension = 11.76 N + 7.20 N

Tension = 18.96 N

Thus, the tension in the wire immediately after the collision is approximately 18.96 N.