a 0.5KG ball is drop at concrete incline which is 45 degree above the horizontal then bounces off with the speed of 5m/s due to the force applied on it what is the change in its momentum?
To determine the change in momentum of the ball, we need to consider the initial momentum before the bounce and the final momentum after the bounce.
1. Initial momentum:
The initial momentum of an object can be calculated using the formula: momentum = mass × velocity.
Given:
Mass (m) = 0.5 kg
Velocity (v) = 0 m/s (ball is dropped, so the initial velocity is 0)
Therefore, the initial momentum of the ball is:
Initial momentum = 0.5 kg × 0 m/s = 0 kg·m/s
2. Final momentum:
To calculate the final momentum after the bounce, we need to determine the final velocity of the ball.
Given:
The angle of incline (θ) = 45 degrees
Initial velocity after the bounce (u) = 5 m/s
To find the final velocity (v) after bouncing, we need to resolve the initial velocity into horizontal and vertical components.
Vertical component: As the ball is bouncing off a 45-degree incline, the vertical component of the initial velocity will remain the same:
Vertical velocity component = Initial velocity × sin(θ)
= 5 m/s × sin(45 degrees)
≈ 5 m/s × 0.707
≈ 3.54 m/s
Horizontal component: The horizontal component of the initial velocity will change direction after bouncing off a vertical surface:
Horizontal velocity component = Initial velocity × cos(θ)
= 5 m/s × cos(45 degrees)
≈ 5 m/s × 0.707
≈ 3.54 m/s
Since momentum is a vector quantity and involves both direction and magnitude, we can calculate the final momentum using the horizontal and vertical components:
Vertical momentum = mass × vertical velocity component
= 0.5 kg × (-3.54 m/s) [negative because the direction is opposite, downward]
= -1.77 kg·m/s
Horizontal momentum remains the same: 0.5 kg × (3.54 m/s) = 1.77 kg·m/s
Finally, to find the total final momentum, we can combine the horizontal and vertical components:
Final momentum = √(Vertical momentum^2 + Horizontal momentum^2)
= √((-1.77 kg·m/s)^2 + (1.77 kg·m/s)^2)
≈ √(3.14 kg^2·m^2/s^2 + 3.14 kg^2·m^2/s^2)
≈ √(6.28 kg^2·m^2/s^2)
≈ 2.51 kg·m/s
3. Change in momentum:
The change in momentum is the difference between the final and initial momenta:
Change in momentum = Final momentum - Initial momentum
= 2.51 kg·m/s - 0 kg·m/s
= 2.51 kg·m/s
Therefore, the change in momentum of the 0.5 kg ball after bouncing is approximately 2.51 kg·m/s.