a force of 200 N is exerted at an angle 30 degrees with respect to the horizontal on an object whose mass is 30kg. the coefficient of friction between the object and the surface is the 0.2.(a)what is the frictional force?(B) what is the acceleration of the object?(c) if the object starts from rest what is the velocity after after 5 seconds ?
F = 200N[30o]
Fx = 200*Cos30 = 173.2 N.
Fy = 200*sin30 = 100 N.
M*g = 30kg * 9.8N/kg = 294 N. = Wt. of
the object.
a. Fk = u*Fn = u*(Mg-Fy) =
0.2(294-100) = 38.8 N. = Force of kinetic friction.
b. a = (Fx-Fk)/M
c. V = Vo + a*t
Vo = 0
a = Value from part b.
t = 5 s.
Solve for V.
A) Frictional force can be found using the equation:
frictional force = coefficient of friction * normal force
The normal force is the force exerted by the surface perpendicular to the object's weight. In this case, it is equal to the object's weight, which can be found using the equation:
weight = mass * gravity
So, weight = 30 kg * 9.8 m/s^2 = 294 N
Now, we can calculate the frictional force:
frictional force = 0.2 * 294 N ≈ 58.8 N
B) The force applied can be broken down into its horizontal and vertical components. The horizontal component can be found using the equation:
horizontal force = force * cos(angle)
Horizontal force = 200 N * cos(30 degrees) ≈ 173.2 N
The net force acting on the object is the horizontal force minus the frictional force:
net force = horizontal force - frictional force
net force = 173.2 N - 58.8 N = 114.4 N
To find the acceleration, we can use Newton's second law:
net force = mass * acceleration
114.4 N = 30 kg * acceleration
acceleration ≈ 3.8 m/s^2
C) If the object starts from rest, we can use the equation of motion:
velocity = initial velocity + acceleration * time
Since the object starts from rest, the initial velocity is 0 m/s. Plugging in the values:
velocity = 0 m/s + 3.8 m/s^2 * 5 s
velocity ≈ 19 m/s
So, the velocity after 5 seconds is approximately 19 m/s.
To solve this problem, we can break down the force exerted into its horizontal and vertical components.
Given:
Force applied (F) = 200 N
Angle (θ) = 30 degrees
Mass (m) = 30 kg
Coefficient of friction (μ) = 0.2
Time (t) = 5 seconds
(a) Frictional force:
To find the frictional force, we need to calculate the normal force (N) first. The normal force is equal to the weight of the object, which is given by the equation:
N = m * g,
where g is the acceleration due to gravity (9.8 m/s^2).
N = (30 kg) * (9.8 m/s^2) = 294 N.
Now, we can calculate the frictional force using the formula:
Frictional force (Ff) = μ * N,
Ff = (0.2) * (294 N) = 58.8 N.
Therefore, the frictional force is 58.8 N.
(b) Acceleration of the object:
To find the acceleration of the object, we need to find the net force acting on it. The net force is given by the equation:
Net force (Fnet) = F * cos(θ) - Ff,
Fnet = (200 N) * cos(30 degrees) - (58.8 N),
Fnet = (200 N) * 0.866 - 58.8 N,
Fnet = 173.2 N - 58.8 N,
Fnet = 114.4 N.
Using Newton's second law (F = m * a), we can find the acceleration:
114.4 N = (30 kg) * a.
a = 114.4 N / 30 kg = 3.81 m/s^2.
Therefore, the acceleration of the object is 3.81 m/s^2.
(c) Velocity after 5 seconds:
To find the velocity of the object after 5 seconds, we can use the following equation of motion:
v = u + a * t,
where v is the final velocity, u is the initial velocity (which is zero in this case), a is the acceleration, and t is the time.
v = 0 + (3.81 m/s^2) * (5 s),
v = 19.05 m/s.
Therefore, the velocity of the object after 5 seconds is 19.05 m/s.
To find the answers to these questions, we'll need to apply some basic principles of physics and use the appropriate formulas. Let's break it down step by step:
(a) What is the frictional force?
The frictional force can be determined using the formula:
Frictional force = Coefficient of friction * Normal force
In this case, the normal force is equal to the weight of the object, which is given by:
Normal force = mass * gravity
Given:
Mass = 30 kg
Gravity (approx.) = 9.8 m/s^2
Coefficient of friction = 0.2
We can now calculate the normal force, and subsequently, the frictional force:
Normal force = 30 kg * 9.8 m/s^2 = 294 N
Frictional force = 0.2 * 294 N = 58.8 N
Therefore, the frictional force is 58.8 N.
(b) What is the acceleration of the object?
To determine the acceleration of the object, we need to resolve the applied force into its horizontal and vertical components. The horizontal component of the force will contribute to accelerating the object, while the vertical component will balance the weight.
Given:
Applied force = 200 N
Angle with respect to the horizontal = 30 degrees
The horizontal component of the applied force can be found using:
Horizontal force = Applied force * cos(theta)
Horizontal force = 200 N * cos(30 degrees) = 200 N * 0.866 = 173.2 N
The net force acting on the object is the horizontal force minus the frictional force:
Net force = Horizontal force - Frictional force
Net force = 173.2 N - 58.8 N = 114.4 N
To calculate the acceleration, we use Newton's second law:
Net force = mass * acceleration
Rearranging the equation, we find the acceleration:
Acceleration = Net force / mass
Acceleration = 114.4 N / 30 kg = 3.8 m/s^2
So, the acceleration of the object is 3.8 m/s^2.
(c) If the object starts from rest, what is the velocity after 5 seconds?
To determine the velocity of the object after 5 seconds, we can use the kinematic equation:
Velocity = Initial velocity + (acceleration * time)
Given:
Initial velocity = 0 m/s (as the object starts from rest)
Acceleration = 3.8 m/s^2
Time = 5 seconds
Plugging in the values into the equation, we get:
Velocity = 0 m/s + (3.8 m/s^2 * 5 s) = 19 m/s
Therefore, the velocity of the object after 5 seconds is 19 m/s.