A 4kg block is lowered down a 37° incline a distance of 5m from point A to point B. A horizontal force (F = 10 N) is applied to the block between A and B as shown in the figure. The kinetic energy of the block at A is 10 J and at B it is 20 J. How much work is done on the block by the force of friction between A and B?
W = +mgsin37(5) + Wf – Fcos37(5) = (4)(9.8)(5)(.6) + Wf – 10(5)(.8) = 77.6 + Wf
W = K = 20 – 10 = 10 J
10 = 77.6 + Wf
Wf = (-77.6+10) = -68 J
Well, the block seems to be on a slippery slope, sliding down like a penguin on an icy hill! Now, let's tackle the question. We know the kinetic energy at point A is 10 J and at point B, it's 20 J.
However, the force of friction is trying to spoil the block's fun by working against it. It's like trying to slide down a water slide while wearing a suit made of Velcro. Not so smooth, huh?
To find the work done by the force of friction, we need to find the difference in kinetic energy (KE) between point A and point B. It's like calculating how much ice cream you've devoured during a picnic.
The increase in kinetic energy is ΔKE = KE(B) - KE(A). So, ΔKE = 20 J - 10 J = 10 J.
Now, here's where the fun part begins. We can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
Therefore, the work done on the block by the force of friction is equal to the negative value of the change in kinetic energy, because friction opposes motion.
In mathematical terms, the work done by friction is -ΔKE. So, the work done by the force of friction is -10 J.
In conclusion, the force of friction did a sneaky little -10 J of work on the block. It might not have been much, but it's enough to ruin the block's slick sliding adventure down the incline!
To find the work done by the force of friction between points A and B, we need to first find the net work done on the block.
The net work done on an object is equal to the change in its kinetic energy. In this case, the kinetic energy of the block changes from 10 J to 20 J.
So, the net work done (W_net) is given by the equation:
W_net = K_B - K_A
Where K_B is the kinetic energy at point B (20 J) and K_A is the kinetic energy at point A (10 J).
Substituting the values, we have:
W_net = 20 J - 10 J
= 10 J
Now, the net work done is the sum of the work done by the applied force (W_applied) and the work done by the force of friction (W_friction). Since the applied force is horizontal, it does not do any work on the block in the vertical direction. Thus, the work done by the applied force is zero.
W_applied = 0 J
Therefore, the work done by the force of friction (W_friction) is equal to the net work done (W_net).
W_friction = W_net
= 10 J
Therefore, the work done on the block by the force of friction between A and B is 10 J.
To find the work done on the block by the force of friction between points A and B, we need to calculate the change in kinetic energy of the block.
The work done is equal to the change in kinetic energy, which can be calculated using the equation:
Work = Change in Kinetic Energy
Given that the kinetic energy of the block at point A is 10 J and at point B is 20 J, the change in kinetic energy can be calculated as:
Change in Kinetic Energy = Kinetic Energy at B - Kinetic Energy at A
Change in Kinetic Energy = 20 J - 10 J
Change in Kinetic Energy = 10 J
Therefore, the work done on the block by the force of friction between points A and B is 10 J.