Asled slides along a horizontal surface on which the coefficient of kinetic friction is 0.25. its velocity at point a is 8.6 m/sm/s and at point b is 5.4 m/sm/s . part a use the impulse-momentum theorem to find how long the sled takes to travel from a to b.

Explanation:

given,

coefficient of kinetic friction, μ = 0.25

Speed of sled at point A = 8.6 m/s

Speed of sled at point B = 5.4 m/s

time taken to travel from point A to B.

we know,

J = F Δ t

J is the impulse

where  F is the frictional force.

t is the time.

we also know that impulse is equal to change in momentum.

frictional force

F = μ N

where as N is the normal force

now,

time taken to move from A to B is equal to 1.31 s

Time taken by the sled is 1.31 s

Solution:

As per the question:

Coefficient of kinetic friction,

Velocity at point A,

Velocity at point A,

Now,

To calculate the time taken by the sled to travel from A to B:

According to the impulse-momentum theorem, impulse and the change in the momentum of an object are equal:

Impulse, I = Change in momentum of the sled,        (1)

                                (2)

where,

F = Force

t = time

p = momentum of the sled

Force on the sled is given by:

where

N = normal reaction force = mg

where

m = mass of the sled

g = acceleration due to gravity

Thus

                    (3)

Using eqn (1), (2) and (3):

t = 1.31 s

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