Calculate the change in momentum in each of the following situations and state the direction of the change in momentum.
a) A 4kg bowling ball strikes a stationary pin head-on at a speed of 3m/s. It continues to move in its original direction, but its speed is reduced to 2m/s.
b) A 200g rubber ball falling vertically strikes ground at a speed of 10m/s and bounces vertically upwards, leaving ground at speed of 6m/s.
c) A 4kg bowling ball moving at 2.5m/s strikes a pin in a glancing fashion. It is deflected through an angle of 10degrees. It's speed is reduced to 2m/s.
Can someone please explain how change in momentum can be calculated first of all and then go over the those questions and please explain what you did.
The change in momentum can be calculated using the formula:
Change in momentum = Final momentum - Initial momentum
The momentum of an object is given by the product of its mass and velocity:
Momentum = mass × velocity
a) For the first situation, we have a 4kg bowling ball striking a stationary pin head-on at a speed of 3m/s. After the collision, the ball continues to move in its original direction, but its speed is reduced to 2m/s.
Initial momentum of the ball = mass × initial velocity = 4kg × 3m/s = 12kg·m/s
Final momentum of the ball = mass × final velocity = 4kg × 2m/s = 8kg·m/s
Change in momentum = Final momentum - Initial momentum = 8kg·m/s - 12kg·m/s = -4kg·m/s
The negative sign indicates that the direction of the change in momentum is opposite to the initial momentum direction.
b) In the second situation, a 200g rubber ball falling vertically strikes the ground at a speed of 10m/s and bounces vertically upwards, leaving the ground at a speed of 6m/s.
Initial momentum of the ball = mass × initial velocity = 0.2kg × 10m/s = 2kg·m/s
Final momentum of the ball = mass × final velocity = 0.2kg × (-6m/s) = -1.2kg·m/s
Change in momentum = Final momentum - Initial momentum = -1.2kg·m/s - 2kg·m/s = -3.2kg·m/s
Again, the negative sign indicates the change in momentum is opposite to the initial momentum direction.
c) For the third situation, a 4kg bowling ball moving at 2.5m/s strikes a pin in a glancing fashion and gets deflected through an angle of 10 degrees. Its speed is reduced to 2m/s.
Since the ball gets deflected, we need to consider the change in both magnitude and direction of the velocity vector.
Initial momentum of the ball = mass × initial velocity = 4kg × 2.5m/s = 10kg·m/s
Final momentum of the ball = mass × final velocity = 4kg × 2m/s = 8kg·m/s
Change in momentum = Final momentum - Initial momentum = 8kg·m/s - 10kg·m/s = -2kg·m/s
Again, the negative sign indicates that the direction of the change in momentum is opposite to the initial momentum direction.
Certainly! The change in momentum can be calculated using the formula:
Change in momentum = Final momentum - Initial momentum
To calculate momentum, we use the equation:
Momentum = mass * velocity
Now, let's go over each situation and calculate the change in momentum and the direction of the change:
a) A 4kg bowling ball strikes a stationary pin head-on at a speed of 3m/s. It continues to move in its original direction, but its speed is reduced to 2m/s.
First, we calculate the initial momentum of the ball:
Initial momentum = mass * initial velocity
= 4kg * 3m/s
= 12 kg.m/s
Next, we calculate the final momentum of the ball:
Final momentum = mass * final velocity
= 4kg * 2m/s
= 8 kg.m/s
Finally, we calculate the change in momentum:
Change in momentum = Final momentum - Initial momentum
= 8 kg.m/s - 12 kg.m/s
= -4 kg.m/s
Since the change in momentum is negative (-4 kg.m/s), it means the momentum of the bowling ball has decreased, indicating a decrease in speed. The direction of the change in momentum is opposite to the initial momentum, so it is in the direction opposite to the motion of the ball.
b) A 200g rubber ball falling vertically strikes the ground at a speed of 10m/s and bounces vertically upwards, leaving the ground at a speed of 6m/s.
First, let's convert the mass of the ball to kilograms:
200g = 0.2kg
Next, we calculate the initial momentum of the ball:
Initial momentum = mass * initial velocity
= 0.2kg * 10m/s
= 2 kg.m/s
Then, we calculate the final momentum of the ball:
Final momentum = mass * final velocity
= 0.2kg * (-6m/s)
= -1.2 kg.m/s
Now, we calculate the change in momentum:
Change in momentum = Final momentum - Initial momentum
= -1.2 kg.m/s - 2 kg.m/s
= -3.2 kg.m/s
Again, the change in momentum is negative (-3.2 kg.m/s), indicating a decrease in momentum and speed. The direction of the change in momentum is opposite to the initial momentum, so it is directed downwards.
c) A 4kg bowling ball moving at 2.5m/s strikes a pin in a glancing fashion. It is deflected through an angle of 10 degrees. Its speed is reduced to 2m/s.
Since the ball strikes the pin in a glancing fashion, its velocity changes both in magnitude and direction. To calculate the change in momentum, we need to calculate the magnitude of the initial and final momenta, as well as the direction of the change.
The change in momentum is given by:
Change in momentum = Final momentum - Initial momentum
First, let's calculate the initial momentum of the ball:
Initial momentum = mass * initial velocity
= 4kg * 2.5m/s
= 10 kg.m/s
Next, we calculate the final momentum of the ball:
Final momentum = mass * final velocity
= 4kg * 2m/s
= 8 kg.m/s
Finally, we calculate the change in momentum:
Change in momentum = Final momentum - Initial momentum
= 8 kg.m/s - 10 kg.m/s
= -2 kg.m/s
Again, we have a negative change in momentum (-2 kg.m/s), indicating a decrease in momentum and speed. The direction of the change in momentum corresponds to the direction of the deflection, which is influenced by the angle of 10 degrees.
I hope this explanation helps you understand how to calculate the change in momentum and determine its direction in different situations!