A little red wagon with mass 8.00 moves in a straight line on a frictionless horizontal surface. It has an initial speed of 3.80 and then is pushed 4.7 in the direction of the initial velocity by a force with a magnitude of 10.0 .
Mass = 8kg
Vo = 3.8 m/s.
d = 4.7 m.
F = 10 N.
F = m*a
a = f/m = 10/8 = 1.25 m/s^2.
V^2 = Vo^2 + 2a*d
V^2 = (3.8)^2 + 2.5*4.7 = 26.19
V = 5.1 m/s = Final velocity.
Well, that little red wagon seems to be having quite the adventure! Moving on a frictionless surface must feel like gliding on butter. Now, let's calculate the final speed of the wagon after it's been pushed.
Using the work-energy principle, we can find the final speed by calculating the work done on the wagon, and then relating it to the change in kinetic energy.
The work done on the wagon can be calculated using the formula:
Work = Force × Displacement × cos(θ)
Since the force and displacement are given, we can substitute those values in and find the work done.
Work = 10.0 × 4.7 × cos(0)
Work = 47.0 Joules
Now, let's consider the change in kinetic energy. The initial kinetic energy (KEi) of the wagon can be calculated using the formula:
KEi = 0.5 × mass × (initial velocity)^2
KEi = 0.5 × 8.00 × (3.80)^2
KEi = 57.44 Joules
The final kinetic energy (KEf) can be calculated using the formula:
KEf = KEi + Work
KEf = 57.44 + 47.0
KEf = 104.44 Joules
Finally, the final speed (vf) can be found using the formula:
vf = sqrt((2 × KEf) / mass)
vf = sqrt((2 × 104.44) / 8.00)
vf ≈ 5.79
So, after being pushed, the little red wagon will be cruising along with a final speed of about 5.79 units. It seems like it's really picking up the pace!
To solve this problem, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object times its acceleration.
Step 1: Find the acceleration of the wagon.
The net force acting on the wagon can be calculated using the equation:
Net Force = mass * acceleration
Given:
Mass of the wagon (m) = 8.00 kg
Force applied (F) = 10.0 N
Using Newton's second law, we can rearrange the equation to solve for acceleration:
acceleration = Net Force / Mass
Substituting the given values:
acceleration = 10.0 N / 8.00 kg
acceleration ≈ 1.25 m/s²
Step 2: Find the final velocity of the wagon.
In this step, we can use the kinematic equation:
Final velocity² = Initial velocity² + 2 * acceleration * distance
Given:
Initial velocity (v₀) = 3.80 m/s
Distance (d) = 4.7 m
Acceleration (a) = 1.25 m/s²
Rearranging the equation, we get:
Final velocity = √(Initial velocity² + 2 * acceleration * distance)
Substituting the given values:
Final velocity = √(3.80 m/s)² + 2 * 1.25 m/s² * 4.7 m
Final velocity ≈ √14.44 m²/s² + 11.70 m²/s²
Final velocity ≈ √26.14 m²/s²
Final velocity ≈ 5.11 m/s
Therefore, the final velocity of the wagon is approximately 5.11 m/s.
To find the final velocity of the little red wagon after it has been pushed, we can use the principle of conservation of momentum. This principle states that the total momentum of a system remains constant if no external forces act on it.
In this case, we have the initial velocity and mass of the wagon, and we also have the force and distance through which the wagon is pushed.
1. First, let's calculate the initial momentum of the wagon:
Momentum (p) = mass (m) × velocity (v)
p1 = 8.00 kg × 3.80 m/s
2. Next, let's calculate the impulse exerted on the wagon:
Impulse (J) = force (F) × time (Δt)
Although the time is not given in this problem, we can still find the impulse using the given force and distance.
J = F × Δt
As the distance (d) is given as 4.7 m, we need to find the time (Δt) it takes for the wagon to be pushed through this distance.
We can use the equation of motion: distance (d) = initial velocity (v1) × time (Δt) + 0.5 × acceleration (a) × time (Δt)^2
Since the acceleration is zero (frictionless surface), the equation simplifies to:
d = v1 × Δt
We can rearrange this equation to solve for Δt:
Δt = d / v1
3. Now that we have the time, let's calculate the impulse:
J = F × Δt
4. The final step is to calculate the final momentum of the wagon:
Momentum (p) = mass (m) × velocity (v)
Since the total momentum is conserved, the initial momentum should be equal to the final momentum:
p1 = p2
(m × v1) = (m × v2)
Solving for v2:
v2 = p1 / m
By following these steps, you will be able to calculate the final velocity (v2) of the little red wagon after it has been pushed.