A mass of 8kg is pulled by a force of 20N along a smooth floor.find
(1) Acceleration
(2)Velocity after 4sec
(3) Distance move in 4sec
(4)Work done by the force
Object of mass 8kg is pulled along a smooth horizontal surface by a string inclined at 30degree to the horizontal.what is the acceleration of the object when tension in the string is 10N
F = m a
a = F/m = 20/8 = 2.5 m/s^2
v = a t = 2.5*4 = 10 meters
d = (1/2) a t^2 = 2.5/2 * 16 = 2.5*8 = 20 meters
work = force * distance in direction of force = 20*20 = 400 Joules
To solve these questions, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
(1) Acceleration:
Using Newton's second law, we can calculate the acceleration of the mass.
F = m * a
20N = 8kg * a
a = 20N / 8kg
a = 2.5 m/s^2
Therefore, the acceleration of the mass is 2.5 m/s^2.
(2) Velocity after 4 seconds:
To find the velocity after 4 seconds, we can use the equation relating velocity, initial velocity, acceleration, and time:
v = u + a*t
Given that the initial velocity is 0 m/s (as the mass starts from rest):
v = 0 + 2.5 m/s^2 * 4s
v = 10 m/s
Therefore, the velocity of the mass after 4 seconds is 10 m/s.
(3) Distance moved in 4 seconds:
We can find the distance by using the equation that relates distance, initial velocity, acceleration, and time:
s = u*t + 0.5*a*t^2
Given that the initial velocity is 0 m/s:
s = 0 * 4s + 0.5 * 2.5 m/s^2 * (4s)^2
s = 0 + 0.5 * 2.5 m/s^2 * 16s^2
s = 0 + 20m
s = 20m
Therefore, the distance moved by the mass in 4 seconds is 20 meters.
(4) Work done by the force:
The work done by a force can be calculated using the equation:
Work = force * distance
Given that the force is 20N and the distance is 20m:
Work = 20N * 20m
Work = 400 Joules
Therefore, the work done by the force is 400 Joules.
To determine the answers to these questions, we can apply Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
(1) Acceleration:
We can find the acceleration using the formula: acceleration (a) = net force (F) / mass (m).
Plugging in the values, we get a = 20N / 8kg = 2.5 m/s².
(2) Velocity after 4 seconds:
To find the velocity, we can use the equation: velocity (v) = initial velocity (u) + acceleration (a) * time (t).
Since the initial velocity is not given, we assume it to be zero as the object starts from rest. Thus, the equation simplifies to v = a * t.
Plugging in the values, we get v = 2.5 m/s² * 4 s = 10 m/s.
(3) Distance moved in 4 seconds:
To find the distance covered, we can use the equation: distance (d) = initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)².
Again, assuming the initial velocity is zero, we simplify the equation to d = 0.5 * a * t².
Plugging in the values, we get d = 0.5 * 2.5 m/s² * (4 s)² = 20 m.
(4) Work done by the force:
The work done by a force can be calculated using: work (W) = force (F) * distance (d) * cos(theta), where theta is the angle between the force vector and the displacement vector. In this case, the force is acting along the displacement, making the angle 0 degrees. Therefore, cos(0) = 1, and the equation simplifies to W = F * d.
Plugging in the values, we get W = 20N * 20m = 400 Joules.
So, the answers to the questions are:
(1) Acceleration = 2.5 m/s²
(2) Velocity after 4 seconds = 10 m/s
(3) Distance moved in 4 seconds = 20 m
(4) Work done by the force = 400 Joules.