A sled slides along a horizontal surface on which the coefficient of kinetic friction is 0.30. Its velocity at point A is 7.6 m/s and at point B is 4.0 m/s. Use the impulse-momentum theorem to find how long (in s) the sled takes to travel from A to B. Assume that the local acceleration due to gravity is -9.80 m/s2.
well: forcefriction*time= mass*changevelocity
mu*mg*time= mass(Va-Vb)
solve for time. Notice mass divides out.
To find the time it takes for the sled to travel from point A to point B using the impulse-momentum theorem, we need to calculate the impulse acting on the sled and divide it by the average force acting on the sled during that time interval.
Impulse can be calculated using the formula:
Impulse = Change in momentum
Momentum is given by:
Momentum = mass × velocity
Since the mass of the sled is not given, we can cancel it out by finding the change in momentum using the formula:
Change in momentum = mass × (final velocity - initial velocity)
Using the given values, we have:
Change in momentum = mass × (4.0 m/s - 7.6 m/s)
Now, we can calculate the average force using the formula:
Average force = Impulse ÷ time
The average force can be determined by multiplying the change in momentum by the acceleration due to gravity (which is negative since it acts in the opposite direction to the sled's motion) and the coefficient of kinetic friction. Therefore:
Average force = Change in momentum × acceleration due to gravity × coefficient of kinetic friction
Finally, we can solve for time by rearranging the formula for average force:
time = Impulse ÷ (Change in momentum × acceleration due to gravity × coefficient of kinetic friction)
Now, let's plug in the given values and calculate the time:
Change in momentum = mass × (4.0 m/s - 7.6 m/s)
Impulse = Change in momentum
Average force = Change in momentum × acceleration due to gravity × coefficient of kinetic friction
time = Impulse ÷ (Change in momentum × acceleration due to gravity × coefficient of kinetic friction)