Problem 1- A 0.5 kg ball is moving to the right at 5 m/s when it is suddenly collide by a wall that exerts on it a horizontal force of 2.5 N for a period of 0.8 s.
a) What is the impulse does the force of the wall exert on the ball?
b) What is the velocity of the ball after the collision?
impulse = change of momentum
= average force * time
= -2.5*.8 = -2 N s = - 2 kg m/s
original momentum = .5*5 = 2.5 kg m/s
final momentum = original momentum + impulse
= 2.5 - 2 = .5
It broke through the wall and is still going right
m v = .5
.5 v = .5
v = 1 m/s
To solve this problem, we need to use the concept of impulse and apply Newton's laws of motion.
a) Impulse is defined as the change in momentum of an object and is equal to the force applied multiplied by the time for which the force is applied. Mathematically, impulse is given by the equation:
Impulse = Force x Time
In this case, the force applied by the wall is 2.5 N and the time for which the force is applied is 0.8 s. Therefore, we can calculate the impulse as follows:
Impulse = 2.5 N x 0.8 s = 2 N·s
Therefore, the impulse exerted by the wall on the ball is 2 N·s.
b) To calculate the velocity of the ball after the collision, we can use the relationship between impulse and momentum. Momentum is defined as the product of an object's mass and its velocity. Mathematically, momentum is given by the equation:
Momentum = Mass x Velocity
The impulse exerted on an object is equal to the change in its momentum. So, we can write:
Impulse = Change in Momentum
Since the ball is initially moving to the right and collides with the wall, its direction of motion changes. Assuming the ball rebounds and moves to the left after the collision, we can write:
Impulse = Final Momentum - Initial Momentum
The initial momentum of the ball is given by the product of its mass (0.5 kg) and initial velocity (5 m/s), which is:
Initial Momentum = 0.5 kg x 5 m/s = 2.5 kg·m/s
Let's assume the velocity of the ball after the collision is v. Then we can write:
Impulse = (0.5 kg x v) - (0.5 kg x (-5 m/s)) = (0.5 kg x v) + 2.5 kg·m/s
Since we already know the impulse is 2 N·s, we can substitute the values into the equation:
2 N·s = (0.5 kg x v) + 2.5 kg·m/s
Now we can solve for v:
0.5 kg x v = 2 N·s - 2.5 kg·m/s
0.5 kg x v = -0.5 kg·m/s
v = (-0.5 kg·m/s) / (0.5 kg)
v = -1 m/s
Therefore, the velocity of the ball after the collision is -1 m/s (moving to the left).