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Friction force, impulse momentum, mass and speed, direction

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1. A sled and rider, gliding over horizontal, frictionless ice at 4.1 m/s, have a combined mass of 70 kg. The sled then slides over a rough spot in the ice, slowing down to 2.6 m/s.
What impulse was delivered to the sled by the friction force from the rough spot?

2. Use the impulse-momentum theorem to find how long (number of sec.) a stone falling straight down takes to increase its speed from 4.5 m/s to 12.5 m/s.

3. Laura, who's mass is 35 kg, jumps horizontally off a 55 kg canoe at 1.5 m/s relative to the canoe. What is the canoe's speed just after she jumps?

4. A spaceship of mass 2.2×106 kg is cruising at a speed of 5.4×106 m/s when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of 5.2×105 kg, is blown straight backward with a speed of 2.5×106 m/s. A second piece, with mass 7.7×105 kg, continues forward at 1.3×106 m/s.

A. What is the speed of the third piece?
B. What is the direction of the third piece? (straight forward or straight backwards)

5. An 8.5 kg dog takes a nap in a canoe and wakes up to find the canoe has drifted out onto the lake but now is stationary. He walks along the length of the canoe at 0.46 m/s, relative to the water, and the canoe simultaneously moves in the opposite direction at 0.17 m/s.
What is the mass of the canoe (in kg)?

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Friction force, impulse momentum, mass and speed and directions are examined.

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1. A sled and rider, gliding over horizontal, frictionless ice at 4.1 m/s, have a combined mass of 70 kg. The sled then slides over a rough spot in the ice, slowing down to 2.6 m/s.
What impulse was delivered to the sled by the friction force from the rough spot?
Solution: Impulse delivered by the rough spot = Fdt = d(mv) = Change in momentum = Final momentum = initial momentum = 70x2.6 - 70x4.1 = - 105 kg.m/s (-ve sign indicates the direction of the impulse is opposite to the direction of motion of the sled)
2. Use the impulse-momentum theorem to find how long (number of sec.) a stone falling straight down takes to increase its speed from 4.5 m/s to 12.5 m/s.
Solution: Impulse momentum theorem states: Impulse = Fdt = Change in momentum .....(1)
Let mass of the stone be m. Acceleration due to gravity g = 9.8 m/s2
Force acting on the stone = F = mg = 9.8m
Initial momentum = 4.5m
Final momentum = 12.5m
Change in momentum = 12.5m - 4.5m = 8m
Substituting F and change in ...

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