a 2.5kg poodle slides across a frozen lake at a speed of 6.3m/s. the coefficient of kinetic friction between poodle and ice is 0.088.
show that the poodle will slide 7.3 seconds before coming to rest.
mg*mu*distance=1/2 m vi^2
but distance= avgvelocity*time=Vi/2*time
mg*mu*vi*time/2= 1/2 m vi^2
time= vi/(g*mu)
To calculate the time it takes for the poodle to slide to a stop, we need to consider the forces acting on it.
First, we need to determine the force of kinetic friction acting on the poodle. The formula to calculate the force of friction is:
Frictional force (F_friction) = coefficient of kinetic friction (μ) * Normal force (N)
The normal force (N) is the force exerted by the poodle perpendicular to the surface of the ice. On a horizontal surface, it is equal to the weight of the poodle. The formula to calculate the normal force is:
Normal force (N) = mass of the poodle (m) * acceleration due to gravity (g)
The acceleration due to gravity is approximately 9.8 m/s^2.
Normal force (N) = 2.5 kg * 9.8 m/s^2 = 24.5 N
Now, we can calculate the force of friction:
F_friction = 0.088 * 24.5 N ≈ 2.156 N
The force of friction acts in the opposite direction to the motion of the poodle, so it will cause the poodle to decelerate.
The force acting to decelerate the poodle is the force of friction, and we can calculate the acceleration (a) using Newton's second law of motion:
F_friction = mass of the poodle (m) * acceleration (a)
Rearranging the equation, we have:
a = F_friction / m
a = 2.156 N / 2.5 kg = 0.8624 m/s^2
Now, we can use the equation of motion to calculate the time it takes for the poodle to stop:
v = u + at
Where:
v = final velocity (0 m/s, as the poodle comes to rest)
u = initial velocity (6.3 m/s)
a = acceleration (-0.8624 m/s^2, as it is opposite to the direction of motion)
t = time
0 = 6.3 m/s + (-0.8624 m/s^2) * t
Rearranging the equation, we have:
t = -6.3 m/s / -0.8624 m/s^2 ≈ 7.3 seconds
Therefore, the poodle will slide for approximately 7.3 seconds before coming to rest.