I calculated parts a, b, c, but cannot figure out d. I tried combining all the forces and adding them but I am missing something?
There is an 18 kg box on a 32degree incline. a HORIZONTAL force of 150 N is given to the box
a) How much work is done by the horizontal force F = 150 N on the 18-kg block of the figure when the force pushes the block 5.1 m up along the 32degree incline? µk = 0.13.
ANSWER: 650 J
b) How much work is done by the gravitational force on the block during this displacement? -480 J
c) How much work is done by the normal force? 0J
d) What is the speed of the block (assume that it is zero initially) after this displacement?
I tried adding up (Fpcostheta - mgcostheta -Ffriction) but it doesn't work
thank you!!
Use the work-energy principle:
Wnet=1/2mv^2-1/2mv^2
Initial velocity is zero therefore:
Wnet=1/2mv^2
Ans: 4.3 m/s
To find the speed of the block after the displacement, you'll need to use the work-energy principle. This principle states that the work done on an object equals the change in its kinetic energy.
To calculate the speed, follow these steps:
Step 1: Determine the work done by the horizontal force. In part a, you found that the work done by the horizontal force (150 N) was 650 J.
Step 2: Calculate the work done against friction. The frictional force can be found using the formula Ffriction = µk * Normal force. In this case, the normal force is equal to the weight of the block, which is mg. Therefore, Ffriction = µk * mg * cosθ. Given that µk = 0.13, the weight (mg) is equal to 18 kg * 9.8 m/s^2, and the angle θ is 32 degrees, you can calculate the value of Ffriction.
Step 3: Find the work done against gravity. The work done against gravity is equal to the gravitational force (weight) times the displacement along the incline. In part b, you found that the work done by gravity was -480 J.
Step 4: Apply the work-energy principle. According to the principle, the total work done on the block is equal to the change in its kinetic energy. Therefore, the equation becomes:
Total work = Work by force + Work against friction + Work against gravity
During the displacement in the inclined plane, the work done by the normal force is zero since it acts perpendicular to the displacement.
Step 5: Calculate the total work done by summing the individual works. In this case, the total work is given by:
Total work = 650 J + Work against friction + (-480 J)
Step 6: Solve the equation for the work done against friction:
Total work = 650 J + Work against friction - 480 J
Simplifying, we get:
Work against friction = Total work - 650 J + 480 J = Total work - 170 J
Substitute the value of the total work and calculate the work done against friction.
Step 7: Determine the change in kinetic energy. The change in kinetic energy is equal to the total work done. Thus, the change in kinetic energy is given by:
Change in kinetic energy = Total work
Step 8: Finally, find the speed of the block using the equation:
Change in kinetic energy = 0.5 * mass * velocity^2
Knowing the mass of the block (18 kg) and the change in kinetic energy from step 7, you can solve for the velocity (speed) of the block.
To find the speed of the block after the displacement, we can use the work-energy theorem. The work done by all the forces should be equal to the change in kinetic energy of the block.
The work done by the horizontal force (F) can be calculated using the formula:
Work = Force * Distance * cos(theta)
Given:
Force (F) = 150 N
Distance = 5.1 m
theta = 32 degrees
So, the work done by the horizontal force is:
Work = 150 N * 5.1 m * cos(32 degrees)
Work = 772.3 J
The total work done on the block can be calculated by adding the work done by the gravitational force and the work done by the frictional force:
Total Work = Work by Gravitational force + Work by Frictional force
Total Work = -480 J + (Coefficient of friction * Normal force * Distance)
Total Work = -480 J + (0.13 * mg * Distance)
However, in part (c), it was correctly mentioned that the work done by the normal force is zero. Therefore, the equation becomes:
Total Work = -480 J + m * g * Distance * sin(theta)
Given:
Mass (m) = 18 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Distance = 5.1 m
theta = 32 degrees
Total Work = -480 J + 18 kg * 9.8 m/s^2 * 5.1 m * sin(32 degrees)
Total Work = -480 J + 883.334 J
Total Work = 403.334 J
Using the work-energy theorem:
Total Work = Change in Kinetic Energy
Change in Kinetic Energy = 1/2 * Mass * (Final Velocity^2 - Initial Velocity^2)
Since the initial velocity is given as zero, we can simplify the equation to:
Change in Kinetic Energy = 1/2 * Mass * Final Velocity^2
Solving for the final velocity:
Final Velocity^2 = (2 * Total Work) / Mass
Final Velocity^2 = (2 * 403.334 J) / 18 kg
Final Velocity^2 = 44.814 J/kg
Final Velocity = √(44.814 J/kg)
Final Velocity = 6.7 m/s
Therefore, the speed of the block after this displacement is approximately 6.7 m/s.