To give a 20-kg child a ride, two teenagers pull on a 3.6-kg sled with ropes, as indicated in the figure. Both teenagers pull with a force of 55 N at an angle of 35 ∘ relative to the forward direction, which is the direction of motion. In addition, the snow exerts a retarding force on the sled that points opposite to the direction of motion, and has a magnitude of 57 N.
I think you're missing the question part.
In any case. You need to break up the force exerted by the teenagers into the horizontal and vertical components. The horizontal force is the only one that makes the sled move. you can make a right angled triangle if you draw it out and use Cos 35 degrees to help find the magnitude of the side you want.
You could probably work out the acceleration if you wanted from that.
how to solve this problem.
To find the acceleration of the sled, 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 multiplied by its acceleration.
The net force can be calculated by subtracting the retarding force from the sum of the forces applied by the teenagers.
1. First, let's calculate the x-component of the force exerted by each teenager:
Fx = Ft * cos(θ)
Where:
Fx is the x-component of the force
Ft is the force exerted by each teenager
θ is the angle between the force and the forward direction of motion
Substituting the values given:
Ft = 55 N
θ = 35°
Fx = 55 N * cos(35°)
Fx ≈ 45.07 N
2. Next, let's calculate the y-component of the force exerted by each teenager:
Fy = Ft * sin(θ)
Where:
Fy is the y-component of the force
Ft is the force exerted by each teenager
θ is the angle between the force and the forward direction of motion
Substituting the values given:
Ft = 55 N
θ = 35°
Fy = 55 N * sin(35°)
Fy ≈ 31.36 N
3. The net force in the x-direction can be calculated by subtracting the retarding force:
ΣFx = Fx - Fret
Where:
ΣFx is the net force in the x-direction
Fx is the x-component of the force
Fret is the retarding force
Substituting the values given:
Fx ≈ 45.07 N
Fret = 57 N
ΣFx = 45.07 N - 57 N
ΣFx ≈ -11.93 N
The negative sign indicates that the net force is in the opposite direction to the intended direction of motion.
4. Since there is no force acting in the y-direction, the net force in the y-direction is zero:
ΣFy = 0
5. Now, we can calculate the net force acting on the sled:
ΣF = √((ΣFx)^2 + (ΣFy)^2)
Substituting the values calculated:
ΣFx ≈ -11.93 N
ΣFy = 0
ΣF = √((-11.93 N)^2 + (0)^2)
ΣF ≈ 11.93 N
6. Finally, we can find the acceleration of the sled using Newton's second law:
ΣF = m * a
Where:
ΣF is the net force acting on the sled
m is the mass of the sled
a is the acceleration of the sled
Substituting the values calculated:
ΣF ≈ 11.93 N
m = 3.6 kg
11.93 N = 3.6 kg * a
a = 11.93 N / 3.6 kg
a ≈ 3.31 m/s²
Therefore, the acceleration of the sled is approximately 3.31 m/s².
To find the acceleration of the sled and the force exerted by the snow, we can break down the forces acting on the sled.
First, let's find the horizontal component of the force exerted by the teenagers on the sled. The horizontal component can be found using the formula:
F_hor = F * cos(theta)
Where F is the magnitude of the force (55 N) and theta is the angle (35 degrees).
F_hor = 55 N * cos(35 degrees)
F_hor ≈ 45.01 N
Next, let's find the net force acting on the sled in the horizontal direction. Since we only have horizontal forces in this problem, the net force is simply the difference between the force applied by the teenagers and the retarding force of the snow.
Net force = F_hor - Retarding force
Net force = 45.01 N - 57 N
Net force ≈ -11.99 N
The negative sign indicates that the net force is in the direction opposite to the motion of the sled.
Now, using Newton's second law of motion, we can determine the acceleration of the sled:
Net force = mass * acceleration
-11.99 N = 3.6 kg * acceleration
acceleration ≈ -3.33 m/s²
Again, the negative sign indicates that the sled is slowing down.
Finally, we can find the force exerted by the snow. Since the retarding force is equal to the net force, we can say:
Retarding force = mass * acceleration
57 N = 3.6 kg * acceleration
acceleration ≈ 15.83 m/s²
The force exerted by the snow is acting in the direction opposite to the motion of the sled.