Question

(Serway 9th ed., 9-3) At one instant, a 17.5-kg sled is moving over a horizontal surface of snow at 3.50 m/s. After 8.75 sec has elapsed, the sled stops. Use a momentum approach to find the average friction force acting on the sled while it was moving. (Ans. 7.00 N)

Answer 1

Using the principle of conservation of momentum and the equation for impulse, we can find the average friction force acting on the sled while it was moving. The average friction force is found to be 7.00 N.

Step-by-step explanation:

To find the average friction force acting on the sled, we can use the principle of conservation of momentum. The initial momentum of the sled is given by its mass multiplied by its initial velocity. The final momentum is zero since the sled comes to a stop. The change in momentum is equal to the impulse, which is equal to the average friction force multiplied by the time. Using these equations, we can solve for the average friction force:

Initial momentum: mi = m × v = 17.5 kg × 3.50 m/s = 61.25 kg·m/s

Final momentum: mf = 0 kg·m/s

Change in momentum: Δp = mf - mi = -61.25 kg·m/s

Impulse: FΔt = Δp

Average friction force: F = Δp / Δt = -61.25 kg·m/s / 8.75 s = -7.00 N

Since the friction force opposes the motion of the sled, we take its magnitude as 7.00 N.

Answer 2

F = 7 N

Step-by-step explanation:

given,

mass of sled = 17.5 Kg

speed of snow on horizontal surface = 3.5 m/s

time taken to stop = 8.75 s

initial momentum

= m U

= 17.5 x 3.5 = 61.25 Kg.m/s

final momentum

final velocity = 0 m/s

final momentum = 0

impulse = change in momentum

impulse = force x time

equating both the formula of impluse

F x t = 61.25 - 0

F x 8.75 = 61.25

F = 7 N

Force acting on the moving sled is equal to F = 7 N