What is the difference between contact force and force at a distance
1 answer:
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Answer:
a) x = v₀ₓ t
, y = t - ½ g t²
Explanation:
This is a projectile launch problem, let's use Newton's second law on each axis
X axis
F = m a
Since there is no acceleration on the x axis, the force on this axis is zero
Y Axis
-W = m
-m g = m
= -g
In this axis the acceleration is the acceleration of gravity
Now we can use science to find the position of the body on each axis
X axis
x = v₀ₓ t + ½ a t²
As the acceleration on this axis is zero
x = v₀ₓ t
Y Axis
y = t + ½
t²
The acceleration on this axis is –g
y = t - ½ g t²
B) to find the maximum value of distance r
r =√ x² + y²
r = √( v₀ₓ² t² + ( t + ½ g t²)²
We can find the maximum value of r using time respect derivatives
dr / dt = 0
0 = ½ 1/√( v₀ₓ² t² + ( t + ½ g t²)² (v₀ₓ² 2t + 2 (
t - ½ g t²)(
- ½ g2t)
We simplify this expression
0 = v₀ₓ² 2t + 2 ( t - ½ g t²) (
- ½ g2t)
-v₀ₓ² t =( t - ½ g t²) (
- ½ g2t)
-v₀ₓ² t = ² t -3/2 gt²
+ 1/2 g² t³
½ g² t²- 3/2 g t =
² + v₀ₓ²
Let's use trigonometry to find go and vox
sin θ = / v₀
cos θ = vox / v₀
= v₀ sin θ
v₀ₓ = v₀ cos θ
We replace
½ g² t² -3/2 g t = v₀ (sin² θ + cos² θ)
g t² - 3v₀ sin θ t = 2 v₀/g
The time is maximum for the angle is zero
Answer:
Explanation:
Force is equal to the product of mass and acceleration.
We know the mass, but not the acceleration. Therefore, we must calculate it before we can calculate force.
1. Calculate Acceleration
Acceleration is the change in velocity over the change in time.
The final velocity is 10 meters per second and the initial velocity is 4 meters per second. The time is 1 second.
Substitute the values into the formula.
Solve the numerator.
Divide.
2. Calculate Force
Now we know the acceleration and the mass.
Substitute the values into the fore formula.
Multiply.
- 1 kilogram meter per square second is equal to 1 Newton.
- Our answer of 12 kg*m/s² is equal to 12 Newtons
The force applies to the ball was <u>12 Newtons.</u>