A 0.243 kg puck, initially at rest on a horizon-

tal, frictionless surface, is struck by a 0.196 kg
puck moving initially along the x axis with
a speed of 3.16 m/s. After the collision, the
0.196 kg puck has a speed of 2.16 m/s at an
angle of 40� to the positive x axis.
Determine the velocity of the 0.243 kg puck
after the collision.
Answer in units of m/s

Find solution in the post

Tom on Saturday, October 22, 2011 at 12:04am.

To determine the velocity of the 0.243 kg puck after the collision, we can apply the principle of conservation of linear momentum. According to this principle, the total momentum before the collision must be equal to the total momentum after the collision.

The momentum, represented by the symbol P, is defined as the product of an object's mass and its velocity. Mathematically, P = m * v, where m is the mass and v is the velocity.

Before the collision:
The initial velocity of the 0.243 kg puck is given as 0 m/s (since it is at rest).

The momentum of the 0.196 kg puck, moving initially along the x-axis with a speed of 3.16 m/s, can be calculated as:
P1 = (0.196 kg) * (3.16 m/s)

After the collision:
The velocity of the 0.196 kg puck is given as 2.16 m/s at an angle of 40 degrees to the positive x-axis.

To determine the components of the velocity of the 0.196 kg puck along the x-axis and y-axis, we use simple trigonometry:
vx = v * cos(theta)
vx = 2.16 m/s * cos(40 degrees)

Similarly, vy = v * sin(theta)
vy = 2.16 m/s * sin(40 degrees)

Now, we have the velocities of both pucks after the collision. Let's call the velocity of the 0.243 kg puck as V1 and the velocity of the 0.196 kg puck as V2.

The total momentum before the collision is equal to the total momentum after the collision:
(0.196 kg * 3.16 m/s) + (0 kg * 0 m/s) = (0.196 kg * vx) + (0.243 kg * V1) + (0.196 kg * vy)

Simplifying this equation, we get:
(0.196 kg * vx) + (0.196 kg * vy) = (0.196 kg * 2.16 m/s * cos(40 degrees)) + (0.243 kg * V1)

Now, using the given values, we can solve for V1:
(0.196 kg * 2.16 m/s * cos(40 degrees)) + (0.196 kg * vy) = (0.243 kg * V1)

Substituting the calculated values for vx and vy, we can solve for V1:
(0.196 kg * 2.16 m/s * cos(40 degrees)) + (0.196 kg * 2.16 m/s * sin(40 degrees)) = (0.243 kg * V1)

Solving this equation will give us the velocity of the 0.243 kg puck after the collision.