Two toy ducks attached to each other by a string, are being pulled by a child. The front duck is m1= 5.0 kg and the back duck is m2= 2.0 kg. The happy guy pulls them with a force of 10 N and friction exists. The toys are moving with constant velocity.
A) if the coefficient of kinetic friction is = 0.12, find the force of friction which is acting on the second duck.
B) calculate the tension in the string connecting the ducks
A) Well, well, well. Looks like we have some ducks on a string getting pulled by a happy child. To find the force of friction on the second duck, we can use the equation F_friction = μ_k * F_normal, where F_friction is the force of friction, μ_k is the coefficient of kinetic friction, and F_normal is the normal force.
Now, the normal force acting on the second duck is equal to its weight (m2 * g), where g is the acceleration due to gravity (about 9.8 m/s^2). So, F_normal = m2 * g.
Once we have the normal force, we can plug it into the equation to find the force of friction. F_friction = μ_k * F_normal.
Let's calculate it. F_normal = 2.0 kg * 9.8 m/s^2 = 19.6 N.
F_friction = 0.12 * 19.6 N = 2.35 N.
Therefore, the force of friction acting on the second duck is 2.35 N. That friction can be quite a quacky situation!
B) Oh, now we're talking about tension in the string! To find the tension, we need to consider the forces acting on the ducks. We have the force applied by the happy child pulling them (10 N), the force of friction on the second duck (2.35 N), and the tension in the string connecting the ducks.
Since the toys are moving with constant velocity, we know that the net force acting on them is zero. The tension in the string (let's call it T) and the force applied by the happy child need to balance out the force of friction on the second duck.
So, T - F_friction = F_applied.
Let's plug in the values. T - 2.35 N = 10 N.
Rearranging the equation, we get T = 10 N + 2.35 N = 12.35 N.
Therefore, the tension in the string connecting the ducks is 12.35 N. Looks like those ducks are feeling the pull of the tension between them!
A) To find the force of friction acting on the second duck, we can use the equation:
Force of friction = coefficient of friction * normal force
The normal force is equal to the weight of the second duck, which can be calculated using the formula:
Weight = mass * gravitational acceleration
For the second duck:
m2 = 2.0 kg (mass)
g = 9.8 m/s^2 (gravitational acceleration)
Weight2 = m2 * g
= 2.0 kg * 9.8 m/s^2
= 19.6 N
Now, we can calculate the force of friction on the second duck:
Force of friction = coefficient of friction * normal force
= 0.12 * 19.6 N
= 2.352 N
Therefore, the force of friction acting on the second duck is 2.352 N.
B) To calculate the tension in the string connecting the ducks, we need to consider the forces acting on the first duck.
The force of tension in the string pulls the front duck forward, opposing the force of friction acting on it. So, the tension force and friction force on the first duck are equal in magnitude and opposite in direction.
Since the ducks are moving with a constant velocity, the net force on the first duck is zero.
Net force = Tension - Force of friction
Since the net force is zero, the tension force and the force of friction are equal:
Tension = Force of friction
Therefore, the tension in the string connecting the ducks is also 2.352 N.
To find the force of friction acting on the second duck, we need to use the equation for friction force:
Friction force = coefficient of friction * normal force
First, let's find the normal force acting on the second duck. The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the normal force is equal to the gravitational force acting on the second duck.
Normal force (N2) = mass of the second duck (m2) * acceleration due to gravity (g)
Given that the mass of the second duck (m2) is 2.0 kg and acceleration due to gravity (g) is approximately 9.8 m/s^2, we can find the normal force.
N2 = 2.0 kg * 9.8 m/s^2
N2 = 19.6 N
Now, using the coefficient of friction (μ = 0.12) and the normal force (N2 = 19.6 N), we can calculate the force of friction (Ffriction) acting on the second duck.
Ffriction = μ * N2
Ffriction = 0.12 * 19.6 N
Ffriction = 2.352 N
Therefore, the force of friction acting on the second duck is 2.352 N.
To calculate the tension in the string connecting the ducks, we need to consider the net force acting on the first duck.
Net force = force applied (10 N) - force of friction acting on the first duck
Since the toys are moving with constant velocity, the net force is zero. Therefore,
0 = 10 N - force of friction acting on the first duck
Let's find the force of friction acting on the first duck:
Ffriction = μ * Normal force
Ffriction = μ * (mass of the first duck * acceleration due to gravity)
Ffriction = 0.12 * (5.0 kg * 9.8 m/s^2)
Ffriction = 5.88 N
Now, we can calculate the tension in the string connecting the ducks:
Tension in the string = force applied - force of friction acting on the first duck
Tension in the string = 10 N - 5.88 N
Tension in the string = 4.12 N
Therefore, the tension in the string connecting the ducks is 4.12 N.