A sled and rider, gliding over horizontal, frictionless ice at 4.9{\rm m/s} , have a combined mass of 86{\rm kg} . The sled then slides over a rough spot in the ice, slowing down to 2.1{\rm m/s}
What impulse was delivered to the sled by the friction force from the rough spot?
To find the impulse delivered to the sled by the friction force, we can use the impulse-momentum principle, which states that the impulse delivered to an object is equal to its change in momentum.
The change in momentum of the sled can be calculated as the product of its mass and the change in velocity:
Change in momentum = mass × change in velocity
Given:
Mass of the sled and rider (m) = 86 kg
Initial velocity of the sled (u) = 4.9 m/s
Final velocity of the sled (v) = 2.1 m/s
Change in velocity = v - u
Change in velocity = 2.1 m/s - 4.9 m/s
Change in velocity = -2.8 m/s (negative sign indicates the slowing down of the sled)
Using the formula to calculate the impulse:
Impulse = change in momentum
Impulse = mass × change in velocity
Impulse = 86 kg × -2.8 m/s
Calculating the impulse:
Impulse = -239.2 kg⋅m/s
Therefore, the impulse delivered to the sled by the friction force from the rough spot is -239.2 kg⋅m/s. The negative sign indicates that the impulse acts in the opposite direction of the initial motion of the sled.