On a cold winter morning, a child sits on a sled resting on smooth ice. When the 9.10 kg sled is pulled with a horizontal force of 36.0 N, it begins to move with an acceleration of 2.10 m/s^2.
The 25.0 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.
Find the acceleration of the child relative to the ice.
0.86
To find the acceleration of the child relative to the ice, we need to analyze the forces acting on the child and the sled separately.
Let's consider the sled first. The only horizontal force acting on the sled is the applied force of 36.0 N. According to Newton's second law of motion, the net force on an object is equal to the product of its mass and acceleration (F = m * a). In this case, the mass of the sled is 9.10 kg and the acceleration is 2.10 m/s^2. Therefore, the net force on the sled is:
F_sled = m_sled * a_sled
= 9.10 kg * 2.10 m/s^2
= 19.11 N
Now, let's consider the child. The child is experiencing two forces – the applied force from the sled and the force of friction between the child and the ice, which acts in the opposite direction of motion. Since the child is sliding backward relative to the sled, the force of friction is in the forward direction. The net force on the child is:
F_child = F_applied - F_friction
We already know that F_applied (force applied by the sled) is 36.0 N. However, we need to find the force of friction. To do that, we can use the formula:
F_friction = µ * N
where µ is the coefficient of friction and N is the normal force. The normal force is equal to the weight of the child, which is given by:
N = m_child * g
where m_child is the mass of the child (25.0 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2). Therefore, the normal force is:
N = 25.0 kg * 9.8 m/s^2
= 245 N
Since the child is sliding backward, the force of friction is in the forward direction. Therefore, the net force on the child becomes:
F_child = F_applied - F_friction
= 36.0 N - µ * N
We are given that the acceleration of the child is smaller than that of the sled. Therefore, the net force on the child is smaller than the net force on the sled:
F_child < F_sled
36.0 N - µ * N < 19.11 N
Simplifying this inequality will give us the maximum value for the coefficient of friction (µ) which allows the child to have a smaller acceleration than the sled. With this information, we can calculate the maximum acceleration of the child relative to the ice.
Please note that the question does not provide any information about the coefficient of friction between the child and the ice, so it is currently impossible to determine the exact acceleration of the child relative to the ice.