A 20.0 kg block is being pushed forward on a flat surface with a force of magnitude 45.0 N against a frictional force of 13.0 N.
how would I find the change in kinetic energy after the force has pushed the block 4 meters?
how much work would it take to stop the block?
work done by 45 N force = 45 * 4 = 180 Joules
work lost to friction = 13 * 4 = 52 Joules
so gain in Ke = 180 - 52 = 128 Joules
then to stop you must remove that 128 Joules of Ke. If you just leave it alone the friction will stop it but in more than 4 meters
Well, let me put on my clown nose and entertain you with some answers!
To find the change in kinetic energy, you'll need to calculate the work done on the block. Work done is equal to the force applied multiplied by the distance traveled. So, work done (W) = force (F) × distance (d). In this case, the force is the net force acting on the block, which is the difference between the applied force and the frictional force. Hence, the net force is 45.0 N - 13.0 N = 32.0 N.
So, the work done on the block (W) = net force (32.0 N) × distance (4 m) = 128.0 Joules.
The change in kinetic energy (ΔKE) is equal to the work done. Therefore, the change in kinetic energy after the force has pushed the block 4 meters is 128.0 Joules.
Now, let's move on to stopping the block. When we stop the block, the final kinetic energy will be zero. Therefore, the work done to stop the block is equal to the initial kinetic energy.
The initial kinetic energy (KE) is given by the formula KE = (1/2) × mass × velocity^2. Since the block comes to a stop, the final velocity is zero. So, KE = (1/2) × mass × (initial velocity)^2.
Now, as a clown, I can't provide the initial velocity value. But assuming it's known, you can calculate the initial kinetic energy. The work done to stop the block will be equal to the initial kinetic energy.
I hope that helps, and remember, don't take my clown answers too seriously!
To find the change in kinetic energy after the force has pushed the block 4 meters, you can use the formula for work:
Work = Force × Distance × cos(θ)
where θ is the angle between the force and the displacement. In this case, the force is pushing the block forward, so θ is 0 degrees (or cos(θ) = 1).
Given:
Force = 45.0 N
Distance = 4.0 m
Plugging in the values, we can calculate the work done on the block:
Work = 45.0 N × 4.0 m × cos(0°)
Work = 180.0 N·m
Since work done is equal to the change in kinetic energy, the change in kinetic energy is 180.0 J (Joules).
To find how much work it would take to stop the block, we need to overcome the force of friction. The work done to stop the block is equal in magnitude but opposite in direction to the work done by the frictional force.
Given:
Frictional force = 13.0 N
The work done to stop the block is:
Work = Force × Distance × cos(θ)
= 13.0 N × 4.0 m × cos(180°)
= -52.0 N·m
Since the work done is negative, it indicates that the work is done in the opposite direction of motion. Hence, it would take 52.0 J (Joules) of work to stop the block.
To find the change in kinetic energy after the force has pushed the block 4 meters, you can use the equation:
ΔKE = KE_final - KE_initial
First, let's find the initial kinetic energy (KE_initial) of the block. The formula for kinetic energy is:
KE = (1/2) * m * v^2
Where m is the mass of the block and v is its velocity.
From the problem, we know the mass of the block is 20.0 kg, and we're given the force applied to the block. The net force acting on the block can be found by subtracting the frictional force from the applied force:
net force = applied force - frictional force
= 45.0 N - 13.0 N
= 32.0 N
Using Newton's second law (F = ma), we can find the acceleration of the block:
acceleration = net force / mass
= 32.0 N / 20.0 kg
= 1.6 m/s^2
To find the initial velocity, we can use the kinematic equation:
v^2 = u^2 + 2as
Where u is the initial velocity, a is the acceleration, and s is the displacement.
Since the block starts from rest, the initial velocity (u) is 0 m/s. Substituting known values into the equation, we have:
v^2 = 0 + 2 * 1.6 m/s^2 * 4 m
v^2 = 12.8 m^2/s^2
Taking the square root of both sides, we get:
v = sqrt(12.8 m^2/s^2) ≈ 3.58 m/s
Now that we have the initial velocity, we can calculate the initial kinetic energy:
KE_initial = (1/2) * m * v^2
= (1/2) * 20.0 kg * (3.58 m/s)^2
≈ 128.72 J
Next, let's find the final kinetic energy (KE_final) of the block. We know that the force pushes the block a distance of 4 meters, so we can use work-energy theorem:
Work = change in kinetic energy
Work = force * distance
The force acting on the block is the net force, which we determined earlier to be 32.0 N. The distance traveled by the block is 4 meters. Therefore:
Work = 32.0 N * 4 m
Work = 128 J
Since work is equal to the change in kinetic energy, we can conclude that:
ΔKE = Work = 128 J
So, the change in kinetic energy is 128 Joules after the force has pushed the block 4 meters.
To find the amount of work required to stop the block, we need to bring it to rest.
The final kinetic energy (KE_final) would be zero since the block comes to a stop. Therefore, the work done to stop the block is equal to the initial kinetic energy (KE_initial).
Therefore, the work required to stop the block is 128.72 J.