A 58.0 kg soccer player jumps vertically upwards and heads the 0.45 kg ball as it is descending vertically with(b) If the ball is in contact with the players head for 19 ms, what is the average acceleration of the ball? a speed of 26.0 m/s. If the player was moving upward with a speed of 4.20 m/s just before impact. (a) What will be the speed of the ball immediately after the collision if the ball rebounds vertically upwards and the collision is elastic? (Note that the force of gravity may be ignored during the brief collision time.)
m₁=58 kg, v₁₀=4.2 m/s,
m₂= 0.45 kg, v₂₀= 26 m/s
v₂={ 2m₁v₁₀ - (m₂-m₁)v₂₀}/(m₁+m₂) =
={ 2•58•4.2 - (0.45-58) •26}/(58+0.45)=
=33.9 m/s.
F=m•Δv/t = m•(v₂-v₁)/t =58{33.9-(-26)}19•10⁻³=1.82•10⁵ N.
(b) If the ball is in contact with the players head for 19 ms, what is the average acceleration of the ball?
F=m2•a
I think the value I am getting is too large, what value are you getting?
To find the speed of the ball immediately after the collision, we can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.
Let's break down the problem step by step:
Step 1: Find the total momentum before the collision.
The momentum of the soccer player before the collision can be calculated using the formula:
momentum = mass × velocity
The mass of the soccer player is given as 58.0 kg, and the velocity is given as 4.20 m/s. So, the momentum before the collision of the soccer player is:
momentum of player = 58.0 kg × 4.20 m/s = 243.6 kg·m/s (approximately)
The momentum of the ball before the collision can be calculated using the same formula. The mass of the ball is given as 0.45 kg, and the velocity is given as 26.0 m/s downward. However, since the collision takes place while the ball is descending, we need to consider the downward velocity as negative. So, the momentum before the collision of the ball is:
momentum of ball = 0.45 kg × (-26.0 m/s) = -11.7 kg·m/s (approximately)
The total momentum before the collision is the sum of the momenta of the soccer player and the ball:
total momentum before collision = momentum of player + momentum of ball
= 243.6 kg·m/s + (-11.7 kg·m/s)
= 231.9 kg·m/s (approximately)
Step 2: Find the total momentum after the collision.
Since the collision is elastic and the ball rebounds vertically upwards, the direction of its velocity changes. The property that remains conserved in an elastic collision is kinetic energy.
During the collision, both the soccer player and the ball experience forces exerted on them. These forces cause both of them to experience an acceleration. To find the average acceleration of the ball, we can use the formula:
acceleration = change in velocity / time
The change in velocity of the ball is the difference between the velocity of the ball just before the collision and the velocity of the ball immediately after the collision.
Given:
- The speed of the ball just before the collision is 26.0 m/s downward.
- The time the ball is in contact with the player's head is 19 ms (which can be converted to seconds by dividing by 1000).
We can calculate the change in velocity of the ball during the collision using the formula:
change in velocity = (-26.0 m/s) - velocity of ball immediately after the collision
Since the ball rebounds vertically upwards, the velocity of the ball immediately after the collision would be in the opposite direction and can be represented as a positive value.
Now, calculating the average acceleration of the ball:
acceleration = change in velocity / time
= [(-26.0 m/s) - velocity of ball immediately after the collision] / 0.019 s
Step 3: Apply the conservation of momentum principle.
According to the conservation of momentum principle, the total momentum before the collision is equal to the total momentum after the collision.
total momentum before collision = total momentum after collision
This can be represented as an equation:
momentum of player + momentum of ball = momentum of player + momentum of ball
So, the resulting equation is:
momentum of player + momentum of ball = momentum of player + (mass of ball × velocity of ball immediately after the collision)
From the equation, we can solve for the velocity of the ball immediately after the collision:
momentum of ball = mass of ball × velocity of ball immediately after the collision
Note: The mass of the player doesn't change during the collision, so its momentum remains the same.
To find the velocity of the ball immediately after the collision, we can rearrange the equation as follows:
momentum of ball = mass of ball × velocity of ball immediately after the collision
velocity of ball immediately after the collision = momentum of ball / mass of ball
Substituting the values, we can find the velocity of the ball immediately after the collision:
velocity of ball immediately after the collision = -11.7 kg·m/s / 0.45 kg
Step 4: Calculate the values.
Now that we have all the required equations, we can substitute the given values to get the final answer:
velocity of ball immediately after the collision = (-11.7 kg·m/s) / 0.45 kg
By performing the calculation, we find that the velocity of the ball immediately after the collision is approximately -26.0 m/s. Note that the negative sign indicates that the ball is moving upward.