A 100-kg object rests on a level surface with a coefficient of friction (both kinetic and static) of 0.40. If the initial velocity is 15m/s and the object comes to rest,
(a) how much friction is acting on the object?
(b) What is the objects 's acceleration due to friction?
(c) How long will it take for it to fome rest
(d) how far will it travel before coming to rest?
a = F/100
To solve this problem, we will use the following equations:
1. Friction force (Ff) = coefficient of friction (μ) * normal force (Fn)
2. Normal force (Fn) = mass (m) * gravitational acceleration (g)
3. Acceleration due to friction (af) = friction force (Ff) / mass (m)
4. Final velocity (Vf) = 0
5. Distance traveled (d) = (initial velocity squared (Vi^2) - final velocity squared (Vf^2)) / (2 * acceleration)
Let's solve step by step:
(a) To calculate the friction force:
Friction force (Ff) = coefficient of friction (μ) * normal force (Fn)
Since there is no vertical motion, the normal force (Fn) is equal to the weight of the object:
Normal force (Fn) = mass (m) * gravitational acceleration (g)
Fn = 100 kg * 9.8 m/s^2 = 980 N
Ff = 0.40 * 980 N = 392 N
Therefore, the friction force acting on the object is 392 N.
(b) To calculate the acceleration due to friction:
Acceleration due to friction (af) = friction force (Ff) / mass (m)
af = 392 N / 100 kg = 3.92 m/s^2
Therefore, the acceleration due to friction is 3.92 m/s^2.
(c) To calculate the time it takes for the object to come to rest:
We can use the equation:
Final velocity (Vf) = initial velocity (Vi) + acceleration (a) * time (t)
Since the final velocity is 0, the equation becomes:
0 = 15 m/s + (-3.92 m/s^2) * t
Simplifying for t:
3.92 m/s^2 * t = 15 m/s
t = 15 m/s / 3.92 m/s^2
t ≈ 3.8265 s
Therefore, it will take approximately 3.8265 seconds for the object to come to rest.
(d) To calculate the distance traveled before coming to rest:
We can use the equation:
Distance traveled (d) = (Vi^2 - Vf^2) / (2a)
Since the final velocity is 0, the equation becomes:
d = (15 m/s)^2 / (2 * 3.92 m/s^2)
d = 225 m^2/s^2 / 7.84 m/s^2
d = 28.72 m
Therefore, the object will travel approximately 28.72 meters before coming to rest.
To find the answers to the given questions, we need to apply the laws of physics and use relevant equations. Let's break down each question and find their solutions:
(a) To determine the amount of friction acting on the object, we first need to calculate the normal force. The normal force is equal to the weight of the object, which can be calculated using the formula:
Weight = mass * gravity
Weight = 100 kg * 9.8 m/s^2 (acceleration due to gravity)
Weight = 980 N
The frictional force can then be calculated using the formula:
Frictional force = coefficient of friction * normal force
Frictional force = 0.40 * 980 N
Frictional force = 392 N
Therefore, the friction acting on the object is 392 N.
(b) The acceleration due to friction can be calculated using the formula:
Acceleration due to friction = Frictional force / mass
Acceleration due to friction = 392 N / 100 kg
Acceleration due to friction = 3.92 m/s^2
Therefore, the object's acceleration due to friction is 3.92 m/s^2.
(c) To calculate the time taken for the object to come to rest, we can use the equation of motion:
Final velocity = Initial velocity + (acceleration * time)
0 = 15 m/s + (-3.92 m/s^2 * time)
Rearranging the equation, we get:
Time = (Final velocity - Initial velocity) / (-acceleration)
Time = (0 - 15 m/s) / (-(-3.92 m/s^2))
Time = 15 m/s / 3.92 m/s^2
Time ≈ 3.82 s
Therefore, it will take approximately 3.82 seconds for the object to come to rest.
(d) To find the distance traveled before coming to rest, we can use the equation:
Distance = (Initial velocity * time) + (0.5 * acceleration * time^2)
Distance = (15 m/s * 3.82 s) + (0.5 * (-3.92 m/s^2) * (3.82 s)^2)
Distance ≈ 57.3 m
Therefore, the object will travel approximately 57.3 meters before coming to rest.
To summarize:
(a) The friction acting on the object is 392 N.
(b) The object's acceleration due to friction is 3.92 m/s^2.
(c) It will take approximately 3.82 seconds for the object to come to rest.
(d) The object will travel approximately 57.3 meters before coming to rest.
F = .4 * 100 * 9.81
a = 100
v = 15 - a t
so t = 15/a
average speed = 15/2 = 7.5
d = 7.5 t