You throw a 6.2 bowling ball down a bowling alley. The ball is in your hand for a distance of 1.5 meters. Its speed increases from 0 to 16m/s(36mph). How much force did you apply?
a=(v²-v₀²)/2s=v²/2s
F=ma
depends on how high you lifted the ball. Gravity did some of the work on the way down.
To determine the force applied to the bowling ball, you can use Newton's second law of motion, which states that force (F) equals mass (m) multiplied by acceleration (a). The acceleration can be calculated using the equation:
a = (final velocity - initial velocity) / time
Given that the initial velocity (u) is 0 m/s, the final velocity (v) is 16 m/s, and the distance (d) covered is 1.5 meters, we can use the equation:
v^2 = u^2 + 2ad
Solving for acceleration (a):
a = (v^2 - u^2) / (2d)
Substituting the values:
a = (16^2 - 0) / (2 * 1.5)
a = 256 / 3 ≈ 85.33 m/s^2
Next, we need to determine the mass (m) of the bowling ball to calculate the force. Let's assume a mass of 6.2 kg.
Finally, we can calculate the force (F) using Newton's second law:
F = m * a
F = 6.2 kg * 85.33 m/s^2
F ≈ 529.09 N
Therefore, the force applied to the bowling ball is approximately 529.09 Newtons.
To determine the amount of force applied to the bowling ball, you can use Newton's second law of motion, which states that force (F) is equal to the mass (m) of an object multiplied by its acceleration (a). In this case, the force applied to the bowling ball can be calculated by finding the change in momentum.
The momentum (p) of an object can be calculated using the formula:
p = m * v
where
p = momentum,
m = mass, and
v = velocity.
In this scenario, the bowling ball starts from rest (velocity = 0) and reaches a final velocity (v) of 16 m/s. The mass of the bowling ball is not given, so we will assume it to be 6.2 kg based on the information provided.
The change in momentum (∆p) can be calculated using the formula:
∆p = m * ∆v
where
∆p = change in momentum, and
∆v = change in velocity.
Since the ball starts with a velocity of 0 m/s, ∆v would be equal to the final velocity (16 m/s). Therefore,
∆p = 6.2 kg * 16 m/s = 99.2 kg·m/s
Now, to find the force (F), you can use the relationship between force, time, and change in momentum, which is given by:
F = ∆p / ∆t
However, the time (∆t) over which the change in momentum occurs is not provided in the question. Therefore, it is not possible to calculate the exact force applied without knowing the time.