Final answer:
The impulse delivered to the sled by the friction force from the rough spot is calculated using the impulse-momentum theorem, which is the product of mass and change in velocity. The impulse is found to be -91.2 kg•m/s, where the negative sign indicates the direction opposite to the initial motion.
Step-by-step explanation:
To calculate the impulse delivered to the sled by the friction force from the rough spot on the ice, we use the impulse-momentum theorem. This theorem states that the impulse on an object is equal to the change in momentum of the object. The formula for impulse (I) is I = Δp where Δp represents the change in momentum. Momentum (p) is the product of mass (m) and velocity (v).
The question states that the sled and rider have a combined mass of 76 kg and the velocities before and after passing the rough spot are 4.4 m/s and 3.2 m/s, respectively. Therefore, we can calculate the change in momentum as follows:
Δp = p_final - p_initial
Δp = m • v_final - m • v_initial
Δp = (76 kg)(3.2 m/s) - (76 kg)(4.4 m/s)
Δp = 243.2 kg•m/s - 334.4 kg•m/s
Δp = -91.2 kg•m/s
The negative sign indicates that the impulse acted in the opposite direction of the sled's initial motion. This is the impulse delivered to the sled by the friction from the rough spot on the ice.