A box of mass 7.0kg is accelerated from resr across a floor at a rate of 4.0m/s2 for 5.0s. Find the net work done on the box.
Fn = ma = 7 * 4 = 28N.
d=Vo*t + 0.5*at^2.
d = 0 + 0.5*4*5^2 = 50m.
W = Fd = 28 * 50m = 1400 Joules.
Well, that box must be really excited to be accelerated from rest! Let's calculate the net work done on this thrill-seeker.
We can find the net work done using the formula:
Net work done = change in kinetic energy
Since the box starts from rest, its initial kinetic energy is zero. The final kinetic energy can be calculated using the formula:
Final kinetic energy = (1/2) * mass * velocity^2
So, let's plug in the given values:
Final kinetic energy = (1/2) * 7.0 kg * (4.0 m/s)^2
Final kinetic energy = 56 J
Since the initial kinetic energy is zero, the change in kinetic energy is equal to the final kinetic energy:
Change in kinetic energy = 56 J
Therefore, the net work done on the box is 56 Joules. It looks like the floor did quite a workout to give the box that energy boost!
To find the net work done on the box, we can use the formula:
Net work = force × distance
First, we need to find the force acting on the box. We can use Newton's second law of motion:
Force = mass × acceleration
Given:
Mass of the box (m) = 7.0 kg
Acceleration (a) = 4.0 m/s^2
So, the force (F) = mass × acceleration = 7.0 kg × 4.0 m/s^2 = 28.0 N
Next, we need to find the distance over which the force is applied. We can use another equation:
Distance = initial velocity × time + (1/2) × acceleration × time^2
Given:
Initial velocity (u) = 0 m/s (as the box is at rest)
Time (t) = 5.0 s
Acceleration (a) = 4.0 m/s^2
Using the equation, distance = 0 × 5.0 + (1/2) × 4.0 × (5.0)^2 = 0 + (1/2) × 4.0 × 25.0 = 0 + 2.0 × 25.0 = 50.0 m
Now, we have the force (F) = 28.0 N and the distance (d) = 50.0 m.
Substituting these values into the formula, we get:
Net work = force × distance = 28.0 N × 50.0 m = 1400 J
Therefore, the net work done on the box is 1400 joules (J).
To find the net work done on the box, we need to use the formula:
Net work = Force x Distance
First, we need to find the force applied on the box. We can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration:
Force = mass x acceleration
Given:
Mass (m) = 7.0 kg
Acceleration (a) = 4.0 m/s^2
Substituting the values into the formula, we get:
Force = 7.0 kg x 4.0 m/s^2
Force = 28 N
Now, we need to find the distance traveled by the box. We can use another formula of motion, which relates distance, initial velocity, final velocity, and time:
Distance = (1/2) x (initial velocity + final velocity) x time
However, in this case, the box starts from rest (initial velocity = 0), so the formula simplifies to:
Distance = (1/2) x final velocity x time
Given:
Time (t) = 5.0 s
Acceleration (a) = 4.0 m/s^2
We can use the kinematic equation vf = vi + at to find the final velocity:
vf = 0 + (4.0 m/s^2) x (5.0 s)
vf = 20 m/s
Substituting the values into the formula, we get:
Distance = (1/2) x (20 m/s) x (5.0 s)
Distance = 50 m
Now, we can calculate the net work done on the box:
Net work = Force x Distance
Net work = 28 N x 50 m
Net work = 1400 Joules
Therefore, the net work done on the box is 1400 Joules.