A 0.15 kg ball of dough is thrown straight up into the air with an initial velocity of 13 m/s.
(a) Find the momentum of the of dough at its maximum height.
kg·m/s upward
(b) Find the momentum of the ball of dough halfway to its maximum height on the way up.
kg·m/s upward
(a) At its maximum height, the vertical component of velocity is zero. Since there is no horizontal component, the magnitude of velocity (speed) and momentum are also zero.
(b) Half way up, the speed is 1/sqrt2 = 70.7% of the original value. (Conservation of energy should tell you why).
Compute the corresponding momentum,
M*V=(0.15)(0.707)*13 = ?
1.379
To find the momentum of the dough at its maximum height, we need to consider that at the highest point of its trajectory, the velocity of the dough will be zero.
(a) The momentum of an object can be calculated using the formula:
momentum = mass × velocity
The mass of the dough is given as 0.15 kg, and since at the maximum height the velocity is zero, the momentum of the dough at its maximum height is:
momentum = 0.15 kg × 0 m/s = 0 kg·m/s (upward)
(b) To find the momentum of the dough halfway to its maximum height, we need to determine its velocity at that point. Since the initial velocity is 13 m/s and the velocity decreases uniformly as the dough moves upwards, the velocity halfway to the maximum height would be half of the initial velocity.
velocity halfway to maximum height = 13 m/s ÷ 2 = 6.5 m/s
Now we can calculate the momentum using the same formula:
momentum = mass × velocity
momentum = 0.15 kg × 6.5 m/s = 0.975 kg·m/s (upward)
To answer this question, we need to understand the concept of momentum.
(a) Momentum is defined as the product of an object's mass and its velocity. In this case, the ball of dough has a mass of 0.15 kg and is thrown straight up with an initial velocity of 13 m/s. At its maximum height, the ball temporarily comes to rest before falling back down. At this point, its velocity is 0 m/s.
To find the momentum at its maximum height, we can use the formula:
Momentum = mass x velocity
For this question, the mass is given as 0.15 kg and the velocity is 0 m/s.
Momentum = 0.15 kg x 0 m/s = 0 kg·m/s
Therefore, the momentum of the ball of dough at its maximum height is 0 kg·m/s upward.
(b) Halfway to its maximum height on the way up, the ball's velocity is not given, so we need to calculate it.
Since the ball is thrown straight up with an initial velocity of 13 m/s, it will decelerate uniformly due to the force of gravity. At the halfway point, its velocity will be halfway between its initial velocity and 0 m/s.
To find the velocity halfway to its maximum height, we can calculate it as:
Velocity halfway = (Initial velocity + Final velocity) / 2
We know the initial velocity is 13 m/s and the final velocity is 0 m/s.
Velocity halfway = (13 m/s + 0 m/s) / 2 = 6.5 m/s
Now that we have the velocity halfway to its maximum height, we can find the momentum using the same formula as before:
Momentum = mass x velocity
The mass of the ball is 0.15 kg, and the velocity halfway is 6.5 m/s.
Momentum = 0.15 kg x 6.5 m/s = 0.975 kg·m/s upward
Therefore, the momentum of the ball of dough halfway to its maximum height on the way up is 0.975 kg·m/s upward.