A 25.0kg pickle is accelerated from rest through a distance of 6.0m in 4.0s across a level floor. If the friction force between the pickle and the floor is 3.8N, how much work is required to move the object?
d = Vo*t + 0.5a*t^2 = 6 m.
0 + 0.5a*4^2 = 6
8a = 6
a = 0.75 m/s^2.
Fnet=m*a
Fnet=25*0.75=18.75 N
Fnet=Fap-Ff
Fap=Fnet+Ff
Fap=18.75+3.8=22.55 N
W=Fap*d
W=22.55*6=135.3 J
To calculate the work required to move the object, we need to consider the net force acting on it and the distance over which the force is applied.
The net force acting on the object can be calculated using Newton's second law:
Net Force (F_net) = mass (m) x acceleration (a)
Since the pickle is accelerated from rest, its acceleration can be determined using the kinematic equation:
acceleration (a) = (final velocity - initial velocity) / time
Since the pickle starts from rest, its initial velocity (v_initial) is 0, and the final velocity (v_final) can be determined using the equation:
v_final = a * time
First, let's find the acceleration of the pickle:
acceleration (a) = (v_final - v_initial) / time
= (v_final - 0) / 4.0s
= v_final / 4.0s
To find the final velocity, we can use the equation:
v_final = a * time
Since the initial velocity is 0:
v_final = a * 4.0s
Now, let's calculate the final velocity:
v_final = a * 4.0s
To calculate the acceleration, we need to use the formula:
F_net = m * a
Now, let's substitute the given values into the formula:
3.8N = 25.0kg * a
Solving for a:
a = 3.8N / 25.0kg
Substituting this value of a into the equation v_final = a * 4.0s, we can find the final velocity.
Finally, we can calculate the work done:
Work (W) = force (F_net) * distance (d)
Substituting the calculated value of F_net and the given distance, we can find the work done.
To find the work required to move the object, we first need to calculate the net force acting on the pickle and then use it to calculate the work done.
The net force acting on an object can be calculated using Newton's second law:
F_net = ma
where F_net is the net force, m is the mass of the object, and a is the acceleration.
In this case, the pickle is accelerated from rest, so the final velocity is unknown. However, we can use the equation for displacement to find the acceleration:
s = ut + (1/2)at^2
where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time.
In this case, the initial velocity is 0 m/s, the displacement is 6.0 m, and the time is 4.0 s. Rearranging the equation, we can solve for the acceleration:
a = 2s / t^2
a = 2(6.0 m) / (4.0 s)^2
a = 2(6.0 m) / 16.0 s^2
a = 12.0 m / 16.0 s^2
a = 0.75 m/s^2
Now that we have the acceleration, we can calculate the net force:
F_net = ma
F_net = (25.0 kg)(0.75 m/s^2)
F_net = 18.75 N
The net force acting on the pickle is 18.75 N.
To calculate the work done, we use the equation:
Work = Force x Distance x cos(theta)
where Work is the work done, Force is the net force, Distance is the displacement, and theta is the angle between the force and the displacement.
In this case, the net force is 18.75 N, the displacement is 6.0 m, and theta is 0 degrees (cos(0) = 1).
Work = (18.75 N)(6.0 m)(cos(0))
Work = 112.5 Joules
Therefore, the amount of work required to move the object is 112.5 Joules.
d = Vo*t + 0.5a*t^2 = 6 m.
0 + 0.5a*4^2 = 6
8a = 6
a = 0.75 m/s^2.
Fp = m*g = 25kg * 9.8N/kg = 245 N. = Force of pickle.
Fap-Fp-Fk = m*a
Fap-245-3.8 = 25*0.75
Fap = 18.75+245+3.8 = 267.6 N. = Force
applied.
Work = Fap * d = 267.6 * 6 = 1605 Joules