A 0.09 kg ball of dough is thrown straight up into the air with an initial speed of 5.5 m/s
(a) Find the momentum of the ball of dough at its maximum height.
(b) Find the momentum of the ball of dough halfway to its maximum height on the way up.
a) the ball has no velocity at the top.
b) You know the KE of the ball at launch. What is the KE half way up? ANS 1/2 the initial.
Then figure v for that KE
Then, don't forget to multiply the velocity by the mass to find the momentum.
To find the momentum of the ball of dough at its maximum height and halfway to its maximum height, we need to apply the principle of the conservation of momentum.
The momentum of an object is defined as the product of its mass and velocity.
(a) Finding the momentum of the ball of dough at its maximum height:
When the ball reaches its maximum height, its velocity is zero. Therefore, the momentum at maximum height will be zero, as the formula for momentum is mass times velocity.
Momentum = mass × velocity
Momentum = 0.09 kg × 0 m/s
Momentum = 0 kg·m/s
So, (a) the momentum of the ball of dough at its maximum height is 0 kg·m/s.
(b) Finding the momentum of the ball of dough halfway to its maximum height on the way up:
To find the velocity halfway to its maximum height, we need to know the equation for the vertical motion of the ball. In this case, the ball is thrown straight up, so we can use the equation:
v^2 = u^2 + 2as
Where:
v = final velocity (which is zero at the maximum height)
u = initial velocity
a = acceleration (due to gravity, approximately -9.8 m/s^2)
s = displacement (halfway to the maximum height)
Rearranging the equation, we get:
u^2 = v^2 - 2as
Substituting the values:
u^2 = 0 - 2(-9.8 m/s^2)(displacement halfway to the maximum height)
Let's calculate the displacement halfway to the maximum height:
Since displacement halfway is the half of the maximum height, we need to find the maximum height first.
Using the kinematic equation:
v^2 = u^2 + 2as
0 = (5.5 m/s)^2 + 2(-9.8 m/s^2)(displacement at maximum height)
Rearranging the equation for the maximum height:
displacement at maximum height = (5.5 m/s)^2 / (2 * 9.8 m/s^2)
Now, we can find the displacement halfway:
displacement halfway = (displacement at maximum height) / 2
Substituting the values:
displacement halfway = [(5.5 m/s)^2 / (2 * 9.8 m/s^2)] / 2
Now that we have the displacement halfway, we can substitute it into the equation we had previously:
u^2 = 0 - 2(-9.8 m/s^2)(displacement halfway)
Let's calculate that value of u (initial velocity):
u^2 = 0 - 2(-9.8 m/s^2)(displacement halfway)
Finally, calculate the momentum using the mass and the calculated velocity halfway:
Momentum = mass × velocity halfway
Remember to use the initial velocity (halfway up) as the velocity halfway:
Momentum = 0.09 kg × velocity halfway
By calculating the above equation, we can find (b) the momentum of the ball of dough halfway to its maximum height on the way up.