A boy and his sled have a combined mass of 65 kg.
1. What is their acceleration as they start down an icy 22.6º incline with a coefficient of friction equal to 0.10?
2.The boy is pulled back to the top of the hill at a constant speed by a tow rope. What is the tension in the rope?
To solve both of these problems, we can use Newton's second law of motion, which states that the sum of the forces acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). Here's how you can find the answers:
1. What is their acceleration as they start down an icy 22.6º incline with a coefficient of friction equal to 0.10?
To find the acceleration, we need to determine the net force acting on the sled-boy system. The net force can be calculated by subtracting the force of friction from the force component parallel to the incline.
First, calculate the force of gravity acting on the sled-boy system:
Force of gravity (Fg) = mass (m) * acceleration due to gravity (g)
Given that the combined mass of the boy and the sled is 65 kg and the acceleration due to gravity is approximately 9.8 m/s²:
Fg = 65 kg * 9.8 m/s²
Next, determine the force component parallel to the incline. This force is given by:
Force parallel (Fp) = Force of gravity * sin(angle of inclination)
Since the angle of inclination is 22.6º:
Fp = Fg * sin(22.6º)
Now, calculate the force of friction:
Force of friction (Ff) = coefficient of friction * Force of gravity
Given that the coefficient of friction is 0.10:
Ff = 0.10 * Fg
Finally, calculate the net force acting on the sled-boy system:
Net force (Fnet) = Fp - Ff
Now we can substitute the values we calculated and solve for acceleration (a):
Fnet = m * a
a = Fnet / m
Keep in mind that the net force acts downhill, so acceleration will be positive.
2. The boy is pulled back to the top of the hill at a constant speed by a tow rope. What is the tension in the rope?
When the boy is pulled back to the top of the hill at a constant speed, the net force acting on the sled-boy system is zero. The tension in the tow rope is equal in magnitude but opposite in direction to the force of friction.
So, using the same force of friction value we calculated earlier:
Tension in the rope = Force of friction
Substitute the value of the force of friction and calculate accordingly.
Remember, in this case, the tension in the rope acts opposite to the force of friction, so the direction will be opposite to the downhill direction.