A ball of mass 0.50 kg is thrown straight up at 6.0 m/s. (a)What is the initial momentum of the ball? (b) What is the momentum of the ball at its peak? (c)What is the momentum of the ball as it hits the ground
A)P=mv >> 0.50 X 6.0 = 3
B)Peak V=0
C)final momentum = -3
p = mv
at its peak, v=0
same speed as it hits as when it left
(a) Well, the initial momentum of the ball is like a waiter balancing plates on a unicycle - it's all about finding the right groove. To calculate the initial momentum, we multiply the mass of the ball (0.50 kg) by its velocity (6.0 m/s). So, the initial momentum of the ball is 3.0 kg·m/s.
(b) Ah, the peak of the ball's journey, where it momentarily feels like it's on top of the world. At the peak, when the ball is as high as a giraffe with a helium addiction, its velocity is zero. So, the momentum of the ball at its peak will also be zero. It's like a magician making momentum disappear.
(c) And finally, the moment we've all been waiting for, the ball's big finale as it hits the ground. Assuming no bounce or lost energy, the momentum of the ball as it hits the ground is the same as its initial momentum. So, it's like coming full circle – what goes up, must come down, and keep the same momentum all around!
To solve this problem, we can use the equation for momentum:
Momentum = mass × velocity
(a) To find the initial momentum of the ball, we need to find the velocity at the start.
Given:
Mass (m) = 0.50 kg
Initial velocity (v) = 6.0 m/s
Using the equation for momentum:
Momentum = mass × velocity
Initial momentum = 0.50 kg × 6.0 m/s
Initial momentum = 3.0 kg⋅m/s
Therefore, the initial momentum of the ball is 3.0 kg⋅m/s.
(b) At the peak of its motion, the ball momentarily comes to a stop before falling back down. Therefore, its velocity is 0 m/s. Using the equation for momentum:
Momentum = mass × velocity
Momentum at peak = 0.50 kg × 0 m/s
Momentum at peak = 0 kg⋅m/s
Therefore, the momentum of the ball at its peak is 0 kg⋅m/s.
(c) As the ball hits the ground, its final momentum can be calculated using the equation for momentum. However, the direction of the velocity changes. Let's assume the ground is at a reference point of 0 m/s.
Given:
Mass (m) = 0.50 kg
Final velocity (v) = -6.0 m/s (negative because the direction is opposite to the initial velocity)
Using the equation for momentum:
Momentum = mass × velocity
Final momentum = 0.50 kg × (-6.0 m/s)
Final momentum = -3.0 kg⋅m/s
Therefore, the momentum of the ball as it hits the ground is -3.0 kg⋅m/s.
To find the answers to these questions, we need to use the formula for momentum:
Momentum (p) = Mass (m) × Velocity (v)
Let's now calculate the answers step by step:
(a) What is the initial momentum of the ball?
The initial momentum is the momentum of the ball just as it is thrown. Given that the ball has a mass of 0.50 kg and is thrown with a velocity of 6.0 m/s, we can calculate its initial momentum as follows:
Initial momentum = Mass × Velocity
= 0.50 kg × 6.0 m/s
= 3.0 kg·m/s
Therefore, the initial momentum of the ball is 3.0 kg·m/s.
(b) What is the momentum of the ball at its peak?
At the peak of the ball's trajectory, the ball momentarily stops moving before it starts to come back down. Since the ball is not moving at this point, its velocity is 0 m/s. Therefore, the momentum of the ball at its peak is:
Momentum at peak = Mass × Velocity
= 0.50 kg × 0 m/s
= 0 kg·m/s
Hence, the momentum of the ball at its peak is 0 kg·m/s.
(c) What is the momentum of the ball as it hits the ground?
The momentum of the ball as it hits the ground depends on its velocity just before hitting the ground. Assuming no loss of energy, the ball's velocity just before hitting the ground will be the same magnitude as its initial velocity (6.0 m/s), but in the opposite direction. Therefore, the momentum of the ball as it hits the ground is:
Momentum at ground = Mass × Velocity
= 0.50 kg × (-6.0 m/s) [negative because of opposite direction]
= -3.0 kg·m/s
Thus, the momentum of the ball as it hits the ground is -3.0 kg·m/s.