Question

In: Physics

with a velocity v = 4.6i m/s. It the strikes the six ball, which has an...

with a velocity v = 4.6i m/s. It the strikes the six ball, which has an identical mass and is initially at rest. After the collision the eight ball is deflected by an angle of θ = 26° and the six ball is deflected by an angle of Φ = 35°, as shown in the figure.

Part (a) Write an expression for the magnitude of six ball's velocity, in terms of the angles given in the problem and the magnitude of the eight ball's initial velocity, v.

Part (b) What is the magnitude of the velocity, in meters per second, of the six ball?

Part (c) What is the magnitude of the velocity of the eight ball, in meters per second, after the collision?

Solutions

Expert Solution


m1 = m = 0.5 kg               m2 = m = 0.5 kg

befor collision


v1 = 4.6i                   v2 = 0


after collision

v1'x = v1'*cos26                  v2'x = v2'*cos35


v1'y = v1'*sin26                  v2'y = v2'*sin35

from momentum conservation

along y

Piy = Pfy


0 = m1*v1'y + m2*v2'y

v1'y = v2'y

v1'*sin26 = v2'*sin35

v1' = v2'*sin35/sin26......(1)

along x axis

Pix = Pfx


m1*v = m1*v1'x + m2*v2'x

v = v1'*cos26 + v2'*cos35.......(2)

using 1 in 2


v = v2'*sin35*cos26/sin26 + v2'*cos35

v*sin26 = v2'*sin35*cos26 + v2' *cos35*sin26

v*sin26 = v2'*sin(35+26)

v*sin26 = v2'*sin61       <------answer


-------

part(b)


v2' = 4.6*sin26/sin61 = 2.3 m/s <------answer

part(c)

v1' = v2'*sin35/sin26

v1' = 3 m/s <<------answer


Related Solutions

Ball A of mass 0.55 kg has a velocity of 0.65 m/s east. It strikes a...
Ball A of mass 0.55 kg has a velocity of 0.65 m/s east. It strikes a stationary ball, also of mass 0.55 kg. Ball A deflects off ball B at an angle of 37° north of A's original path. Ball B moves in a line 90° right of the final path of A. Find the momentum (in kg m/s) of Ball A after the collision.
ball A of mass 0.55kg has a velocity of 0.65m/s east. it strikes a stationary ball...
ball A of mass 0.55kg has a velocity of 0.65m/s east. it strikes a stationary ball also of mass 0.55kg ball A deflects off ball B at an angle of 37 degrees north of A's original path. ball B moves in a line 90 degree right of the final path of A. find the momentum of ball A and ball B after the collision.
A cue ball (0.17 kg) is moving at a velocity of 11.3 m/s when it strikes...
A cue ball (0.17 kg) is moving at a velocity of 11.3 m/s when it strikes two billiard balls (0.16kg), at rest, "dead center" and comes to rest. If one billiard ball moves at a velocity of 4.1 m/s at an angle of 39 radians measured clockwise relative to the incoming direction of the cue ball, and another ball moves at an angle measured counter-clockwise relative to the incoming direction of the cue ball, how fast is the second ball...
The eight ball, which has a mass of m=0.5kg, is initially moving with a velocity v=4.9i...
The eight ball, which has a mass of m=0.5kg, is initially moving with a velocity v=4.9i m/s. It the strikes the six ball, which has an identical mass and is initially at rest. After the collision the eight ball is deflected by an angle of theta 27 degrees and the six ball is deflected by an angle psi 31 degrees. (a) Write an expression for the magnitude of six ball's velocity, in terms of the angles given in the eight...
Ball A with a mass of 2.0 kilograms is traveling at 8.0 m/s strikes Ball B...
Ball A with a mass of 2.0 kilograms is traveling at 8.0 m/s strikes Ball B with a mass 5.0 kilograms which is at rest. After the collision, Ball A moves away at an angle of 40.0 degrees above the x-axis and Ball B moves away at an angle of -20.0 degrees below the x-axis. What are the final velocities of each ball? Draw and label a sketch of the problem.
A ball of mass m moving with velocity v⃗ i strikes a vertical wall as shown...
A ball of mass m moving with velocity v⃗ i strikes a vertical wall as shown in (Figure 1). The angle between the ball's initial velocity vector and the wall is θi as shown on the diagram, which depicts the situation as seen from above. The duration of the collision between the ball and the wall is Δt, and this collision is completely elastic. Friction is negligible, so the ball does not start spinning. In this idealized collision, the force...
1. A billiard ball moving at 5.80 m/s strikes a stationary ball of the same mass....
1. A billiard ball moving at 5.80 m/s strikes a stationary ball of the same mass. After the collision, the first ball moves at 4.81 m/s at an angle of 34.0° with respect to the original line of motion. Assuming an elastic collision (and ignoring friction and rotational motion), find the struck ball's velocity after the collision. (a)magnitude_____ m/s (b) direction_____ ° (with respect to the original line of motion) 2. A rod of length 36.00 cm has linear density...
A ball of mass 500g is shot with an initial velocity of 10 m/s. the ball...
A ball of mass 500g is shot with an initial velocity of 10 m/s. the ball hits a pendulum bob (initially at rest) of mass of 2kg and the collision is perfectly elastic. a) find the velocity of the pendulum bob immediately after the collision. b) find the length of the pendulum if it comes to rest after turning by an angle of 30 degrees. - Part b is the one I am stuck on!!!
A jet of water 50 mm in diameter with a velocity of 20 m/s strikes a...
A jet of water 50 mm in diameter with a velocity of 20 m/s strikes a flat plate inclined at an angle of 30° to the axis of the jet. Determine (i) the normal force exerted on the plate when the plate is stationary (ii) the normal force exerted on the plate when the plate is moving at 5 m/s in the direction of the jet (iii) the work-done on the plate and the efficiency for case (ii).
A proton with a velocity V = (2.00 m / s) i - (4.00 m /...
A proton with a velocity V = (2.00 m / s) i - (4.00 m / s) j - (1.00 m / s) k, a B = (1.00 T) i + (2.00 T) j- (1.00 T) k it moves within the magnetic field. What is the magnitude of the magnetic force (Fe) acting on the particle? (Qproton = 1.6x10-19 C)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT