A bodyof mass 0.4 if is thrown against a brick wall.when it strikes the wall,it is moving horizontally to the left at 30 m/ s,and it rebounds horizontally to the right at 20 m/ s.find;the change in momentum of ball,magnitude and sign of impulse of the force exerted on the ball,direction of force acting on the ball
initial momentum = 0.4(-30) = -12 kg m/s
final momentum = 0.4 (+20) = +8 kg m/s
change = +8 - -12 = +20 kg m/s
force and impulse to right. impulse = change of momentum and force = impulse / time in contact with wall
Well, well, well. Looks like we have a ball hitting a brick wall with quite the velocity, huh? Let's dive right into it, shall we?
The change in momentum of the ball can be calculated by finding the difference between its initial momentum and final momentum. Now, momentum is just the product of mass and velocity. So, using some good old math, we have:
Initial momentum = mass * initial velocity
Final momentum = mass * final velocity
Plugging the given values, we get:
Initial momentum = 0.4 kg * 30 m/s
Final momentum = 0.4 kg * (-20 m/s) (negative because the rebound is in the opposite direction)
Now, let's calculate the magnitude (absolute value) of the change in momentum:
Change in momentum = Final momentum - Initial momentum
And the sign of impulse of the force exerted on the ball depends on the direction of the force. In this case, since the ball rebounds to the right, the force exerted on the ball is also in the opposite direction, to the left. So, we can say that the impulse acting on the ball is negative (signifying a decrease in momentum).
Now, as for the direction of the force acting on the ball, it's pretty obvious, my friend. Since the ball is hitting the wall and rebounding from it, the force must be acting towards the right, pushing the ball away from the wall.
So, to sum it all up:
- The change in momentum of the ball is the difference between its initial and final momenta.
- The magnitude of the change in momentum is calculated by taking the absolute value of the difference.
- The sign of impulse of the force exerted on the ball is negative because its momentum decreases.
- The force acting on the ball is directed towards the right.
Hope that explanation hit the mark! Keep those questions coming!
To find the change in momentum of the ball, we can use the formula:
Change in momentum = Final momentum - Initial momentum
The momentum of an object is given by the product of its mass and velocity.
Given:
Mass of the ball, m = 0.4 kg
Initial velocity, u = -30 m/s (negative because it's moving to the left)
Final velocity, v = 20 m/s (positive because it rebounds to the right)
Step 1: Calculate the initial momentum
Initial momentum, p_initial = mass x initial velocity
p_initial = 0.4 kg x (-30 m/s)
p_initial = -12 kg·m/s
Step 2: Calculate the final momentum
Final momentum, p_final = mass x final velocity
p_final = 0.4 kg x 20 m/s
p_final = 8 kg·m/s
Step 3: Calculate the change in momentum
Change in momentum = p_final - p_initial
Change in momentum = 8 kg·m/s - (-12 kg·m/s)
Change in momentum = 8 kg·m/s + 12 kg·m/s
Change in momentum = 20 kg·m/s
The magnitude of the change in momentum is 20 kg·m/s, and since the final momentum is positive while the initial momentum is negative, the sign of the change in momentum is positive.
Next, let's calculate the impulse of the force exerted on the ball. Impulse is defined as the change in momentum of an object during a collision.
Impulse = Change in momentum
Since the change in momentum is 20 kg·m/s, the impulse of the force exerted on the ball is also 20 kg·m/s.
Finally, let's determine the direction of the force acting on the ball. The direction of the force is related to the change in momentum.
Since the ball rebounds from left to right, the force exerted on the ball is directed from right to left.
Therefore, the direction of the force acting on the ball is to the left.
To find the change in momentum of the ball, we can use the equation:
Change in Momentum = Final Momentum - Initial Momentum
The momentum of an object is given by the product of its mass and velocity. In this case, the mass of the ball is 0.4 kg and its initial velocity is 30 m/s to the left. The final velocity of the ball is 20 m/s to the right.
Initial Momentum = mass * initial velocity
Initial Momentum = 0.4 kg * (-30 m/s)
Initial Momentum = -12 kg·m/s
Final Momentum = mass * final velocity
Final Momentum = 0.4 kg * 20 m/s
Final Momentum = 8 kg·m/s
Change in Momentum = Final Momentum - Initial Momentum
Change in Momentum = 8 kg·m/s - (-12 kg·m/s)
Change in Momentum = 20 kg·m/s
Therefore, the change in momentum of the ball is 20 kg·m/s.
Impulse is defined as the change in momentum of an object. The magnitude of impulse can be calculated using the equation:
Impulse = Change in Momentum
In this case, the magnitude of the impulse exerted on the ball is 20 kg·m/s.
The sign of impulse provides information about the direction of the force exerted on the ball. In this case, since the ball changes its velocity from left to right, the impulse is positive (+20 kg·m/s). This indicates that the force exerted by the wall on the ball is in the opposite direction of the initial velocity.
Therefore, the magnitude of the impulse is 20 kg·m/s and the direction of the force acting on the ball is to the right.