On a cold winter morning, a child sits on a sled resting on smooth ice. When the 9.19 kg sled is pulled with a horizontal force of 38.4 N, it begins to move with an acceleration of 2.39 m/s2. The 23.8 kg child accelerates too, but with a smaller acceleration than that of the sled. Thus, the child moves forward relative to the ice, but slides backward relative to the sled. Calculate the acceleration of the child relative to the ice.
The net force acting on the sled is 9.19*2.39=30.0 N, leaving 8.4N acting on the child
8.4N=23.8*a
solve for a
To find the acceleration of the child relative to the ice, 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.
We are given:
Mass of the sled (m1) = 9.19 kg
Force applied to the sled (F) = 38.4 N
Acceleration of the sled (a) = 2.39 m/s^2
Using Newton's second law, we can find the mass of the child (m2):
m1 * a = F
9.19 kg * 2.39 m/s^2 = 38.4 N
m2 * a2 = 38.4 N
a2 = 38.4 N / m2
Now, let's calculate the acceleration of the child relative to the ice by subtracting the acceleration of the sled from the acceleration of the child:
Acceleration of the child relative to the ice (a2 - a) = (38.4 N / m2) - 2.39 m/s^2
However, we still need the mass of the child (m2) to calculate the final answer.
Unfortunately, the problem does not provide the mass of the child, so we cannot directly calculate the acceleration of the child relative to the ice with the given information. We would need the mass of the child to proceed further.
If you have the mass of the child, please provide it, and I will be able to help you calculate the acceleration of the child relative to the ice.