An object has a mass of 2kg and rests on a surface where the coefficient of friction is .2. (a) Find the acceleration of 10 m/sec squared (b) Assume Vi=0, how long does it take to travel 100m? (c) What is the velocity at this time?
To answer these questions, we can use Newton's second law of motion and the equations of motion.
(a) To find the acceleration, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. The force due to friction can be calculated using the equation:
Frictional force = coefficient of friction * normal force
The normal force is equal to the weight of the object, which is the mass of the object multiplied by the acceleration due to gravity (9.8 m/s^2).
Normal force = mass * gravity
Substituting these values into the equation, we get:
Frictional force = coefficient of friction * (mass * gravity)
Now, we can use Newton's second law to find the acceleration:
Force = mass * acceleration
Frictional force = mass * acceleration
Substituting the value of the frictional force, we get:
coefficient of friction * (mass * gravity) = mass * acceleration
Simplifying the equation, we get:
acceleration = coefficient of friction * gravity
Plugging in the given values, we have:
acceleration = 0.2 * 9.8 m/s^2 = 1.96 m/s^2
Therefore, the acceleration is 1.96 m/s^2.
(b) To find the time it takes to travel 100m, we can use the equation of motion:
s = Vit + (1/2)at^2
where s is the distance traveled, Vi is the initial velocity, a is the acceleration, and t is the time.
Since the initial velocity is 0 m/s (Vi = 0), the equation simplifies to:
s = (1/2)at^2
Rearranging the equation, we get:
t^2 = (2s) / a
Substituting the given values, we have:
t^2 = (2 * 100m) / 1.96 m/s^2
t^2 = 204.08
Taking the square root of both sides, we find:
t ≈ 14.29 sec (rounded to two decimal places)
Therefore, it takes approximately 14.29 seconds to travel 100 meters.
(c) To find the velocity at this time, we can use the equation of motion:
Vf = Vi + at
Since the initial velocity is 0 m/s (Vi = 0), the equation simplifies to:
Vf = at
Plugging in the given values, we have:
Vf = 1.96 m/s^2 * 14.29 sec
Vf ≈ 28 m/s (rounded to two decimal places)
Therefore, the velocity at this time is approximately 28 m/s.