A ball of mass m moving with velocity v_i_vec strikes a vertical wall. The angle between the ball's initial velocity vector and the wall is theta_i 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 Deltat, and this collision is completely elastic. Friction is negligible, so the ball does not start spinning. In this idealized collision, the force exerted on the ball by the wall is parallel to the x axis.
Part A:What is the final angle that the ball's velocity vector makes with the negative y axis?
Part B: What is the magnitude of the average force exerted on the ball by the wall?
This question is based on the concepts of force, momentum and elastic collision.
First resolve the initial velocity of ball in the x and y components. Then, calculate the final velocity of the ball and its angle.
Force- on an object is defined as the rate of change of its momentum. This can be expressed as follows:
Here, is the change in momentum of the object in time.
Momentum- of an object is the product of its mass and velocity . This is expressed as follows:
Magnitude of a vector with component and is given by relation;
When two objects collide, transfer of energy and momentum takes place. The wall during collision imparts force on the wall and changes its momentum. The energy of the system (wall and ball) remains conserved during the collision because the collision is elastic.
In the perfectly elastic collision, if two objects of masses and with initial velocities and collide, their final velocities and are expressed as follows:
……(1)
……(2)
Calculate x-component of initial velocity using trigonometric relations as follows:
Similarly, calculate y-component of initial velocity as follows:
Calculate final velocities along x-axis and y-axis by using the relationship (1).
Calculate final velocities along x-axis as follows:
Velocity of object 1 after collision is given by (1).
Substitute for , for , for and for in the equation (1) to calculate the horizontal component of final velocity.
Since mass of wall is much greater than the mass of the ball.
Substitute for in the above equation of .
Only x-component of velocity is involved. Therefore y component of velocity that is remains unchanged. This can be expressed as follows:
Part A
Calculate the angle of the final velocity as follows:
Substitute for and for in the equation to calculate angle of the final velocity.
Here negative sign shows that angle measured is anticlockwise.
Hence, the angle of final velocity is from negative axis.
Calculate change in momentum along x-axis as follows:
Substitute for and for in the equation to calculate change in momentum along x-axis.
No collision takes place in y-direction. y-component of momentum doesn’t change. This can be expressed as follows:
Calculate force along x-axis by using definition of force as follows:
Substitute for in the equation .
Calculate force along y-axis by using definition of force as follows:
Substitute for in the equation .
Part B
Calculate magnitude of the force by using relation of magnitude of a vector as follows:
Substitute for and for in the equation to calculate the magnitude of force.
Hence, the magnitude of force is .
Ans: Part AThe angle of final velocity vector is .
A ball of mass m moving with velocity v_i_vec strikes a vertical wall. The angle between the ball's initial velocity ve...
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...
A Ball Hits a Wall Elastically Part A A ball of mass m moving with velocity strikes a vertical wall as shown in (Figure 1). The angle between the ball's initial velocity vector and the wall is 0, 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 Δ, and this collision is completely elastic. Friction is negligible, so the ball does not start spinning...
A billiard ball moving at 6.00 m/s strikes a stationary ball of the same mass. After the collision, the first ball moves at 4.94 m/s at an angle of 34.5° 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. What is the magnitude of the velocity and the direction o counter-clockwise from the original direction of motion?
A billiard ball moving at 5.60 m/s strikes a stationary ball of the same mass. After the collision, the first ball moves at 5.03 m/s at an angle of 26.0° 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. magnitude m/s direction ° (with respect to the original line of motion)
A billiard ball moving at 6.00 m/s strikes a stationary ball of the same mass. After the collision, the first ball moves at 5.05 m/s at an angle of 32.7° 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. magnitude _____________ m/s direction ____________ ° counter-clockwise from the original direction of motion
A billiard ball moving at 5.30 m/s strikes a stationary ball of the same mass. After the collision, the first ball moves at 4.8 m/s, at an angle of θ = 25.0° with respect to the original line of motion. Assuming an elastic collision (and ignoring friction and rotational motion), find the struck ball's velocity (both magnitude and direction) after the collision. I need a good explanation please. thank you
A 4.50-kg steel ball strikes a wall with a speed of 7.0 m/s at an angle of θ = 60.0° with the surface. It bounces off with the same speed and angle (see figure below). If the ball is in contact with the wall for 0.200 s, what is the average force exerted by the wall on the ball? (Assume right and up are the positive directions.) Fx = N Fy = N
65. A lacrosse ball (m = 0.145 kg) is thrown against a vertical wall at angle, θ = 360, with a velocity of 38 m/s as shown below. Assume a perfectly elastic collision. What is the impulse delivered to the ball by the wall?
A racquet ball with mass m = 0.252 kg is moving toward the wall at v = 18.2 m/s and at an angle of θ = 25° with respect to the horizontal. The ball makes a perfectly elastic collision with the solid, frictionless wall and rebounds at the same angle with respect to the horizontal. The ball is in contact with the wall for t = 0.06 s. 1) What is the magnitude of the initial momentum of the racquet...