a girl pulls a 12.0 kg wagon along by exerting a force of 15.0 N on the wagons handle, which makes an angle of 20.0 degrees with the horizontal. Friction provides a force of 11.0 N in the opposite direction. How long does it take for the wagon, which is initially at rest, to reach a speed of 4.50 m/s?
Well, well, well, it seems we have a wheely interesting situation here! Let's see if we can give you a "wheely" good answer to your question.
To find out how long it takes for the wagon to reach a speed of 4.50 m/s, we can use the good old Newton's second law of motion, which states that force equals mass times acceleration (F = ma).
First, we need to find the net force acting on the wagon. This can be calculated by subtracting the force of friction from the force applied by the girl:
Net force = Force applied - Force of friction
= 15 N - 11 N
= 4 N
But wait, we're not done clowning around yet! We also need to find the acceleration of the wagon. And how do we do that, you ask? By using another handy-dandy equation: Newton's second law, rearranged to solve for acceleration (a = F/m).
Acceleration = Net force / mass
= 4 N / 12.0 kg
= 0.333 m/s²
Alrighty, now we've got everything we need. To find the time it takes for the wagon to reach a speed of 4.50 m/s, we can use the equation of motion (v = u + at), where "v" is the final velocity (4.50 m/s), "u" is the initial velocity (0 m/s), "a" is the acceleration (0.333 m/s²), and we're solving for "t" (time).
4.50 m/s = 0 m/s + (0.333 m/s²)t
Now, let's solve for "t". Drumroll, please...
t = (4.50 m/s) / (0.333 m/s²)
= 13.51 s
So, it takes approximately 13.51 seconds for the wagon to reach a speed of 4.50 m/s. Just remember to factor in some extra time for clowning around!
To find the time it takes for the wagon to reach a speed of 4.50 m/s, we can use Newton's second law of motion and kinematic equations.
Let's break down the forces acting on the wagon:
1. The force exerted by the girl: 15.0 N
2. The force of friction: 11.0 N
The net force acting on the wagon is the vector sum of these forces, given by the formula:
Net force = Force exerted by the girl - Force of friction
Net force = 15.0 N - 11.0 N = 4.0 N
Next, we need to find the acceleration of the wagon using Newton's second law of motion:
Net force = mass × acceleration
4.0 N = 12.0 kg × acceleration
acceleration = 4.0 N / 12.0 kg = 0.33 m/s²
Now, let's find the time it takes for the wagon to reach a speed of 4.50 m/s using the kinematic equation:
v = u + at
Given:
- Initial velocity, u = 0 (since the wagon is initially at rest)
- Final velocity, v = 4.50 m/s
- Acceleration, a = 0.33 m/s²
Substituting these values into the equation, we have:
4.50 m/s = 0 + 0.33 m/s² × t
Simplifying the equation, we can solve for t:
4.50 m/s = 0.33 m/s² × t
t = 4.50 m/s / 0.33 m/s²
t ≈ 13.64 seconds
Therefore, it will take approximately 13.64 seconds for the wagon to reach a speed of 4.50 m/s.
To determine how long it takes for the wagon to reach a speed of 4.50 m/s, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration:
F_net = m * a
In this case, we need to find the acceleration of the wagon. The net force on the wagon is the difference between the force exerted by the girl and the force of friction:
F_net = F_girl - F_friction
The force exerted by the girl can be resolved into horizontal and vertical components. The vertical component of the girl's force cancels out with the vertical component of the force of friction, since the wagon is on a horizontal surface and there is no vertical acceleration. Therefore, we only need to consider the horizontal components:
F_girl_horizontal = F_girl * cos(theta)
F_friction_horizontal = F_friction * cos(180 degrees)
Since the force of friction is acting in the opposite direction, we use the cosine of 180 degrees. Now we can substitute the values given into the equation:
F_net = (F_girl * cos(theta)) - (F_friction * cos(180 degrees))
Next, we can rearrange the equation to solve for the acceleration:
a = F_net / m
Now we can substitute the known values to find the acceleration:
a = [(F_girl * cos(theta)) - (F_friction * cos(180 degrees))] / m
After calculating the acceleration, we can use the kinematic equation to determine the time it takes for the wagon to reach a speed of 4.50 m/s. The kinematic equation relating acceleration, initial velocity, final velocity, and time is:
v_f = v_i + a * t
Since the wagon is initially at rest, the initial velocity (v_i) is 0. Therefore, the equation becomes:
v_f = a * t
Now we can rearrange the equation to solve for time:
t = v_f / a
Finally, we can substitute the values given into the equation to find the time taken for the wagon to reach a speed of 4.50 m/s.
Calculate the acceleration rate, a = F/m. F is the net force in the horizontal direction.
The time required is (4.50 m/s)/a
F = 15 cos 20 - 11 Newtons.