A block of weight = 25.0 N sits on a frictionless inclined plane, which makes an angle = 34.0 with respect to the horizontal, as shown in the figure. A force of magnitude F= 14.0 N, applied parallel to the incline, is just sufficient to pull the block up the plane at constant speed.
What is , the work done on the block by the force of gravity as the block moves a distance = 2.50 m up the incline?
What is , the work done on the block by the applied force as the block moves a distance = 2.50 m up the incline?
give me the answer.
To find the work done on the block by the force of gravity and the applied force, we can use the formulas for work:
Work (W) = Force (F) * Distance (d) * cos(theta)
Where:
- W is the work done
- F is the force
- d is the distance
- theta is the angle between the force and the direction of motion
Given:
- Weight of the block (force of gravity) = 25.0 N
- Angle of the inclined plane = 34.0 degrees
- Applied force = 14.0 N
- Distance moved up the incline = 2.50 m
First, let's find the work done on the block by the force of gravity. We know that the weight of the block acts vertically downward, perpendicular to the incline. Therefore, the angle between the weight and the direction of motion is 90 degrees, and the cosine of 90 degrees is 0.
So, the work done on the block by the force of gravity is:
W_gravity = Weight * Distance * cos(theta)
W_gravity = 25.0 N * 2.50 m * cos(90 degrees)
W_gravity = 0 N
Therefore, the work done on the block by the force of gravity is 0 J (joules).
Now, let's find the work done on the block by the applied force. The applied force acts parallel to the incline, so the angle between the applied force and the direction of motion is 0 degrees.
So, the work done on the block by the applied force is:
W_applied = Applied force * Distance * cos(theta)
W_applied = 14.0 N * 2.50 m * cos(0 degrees)
W_applied = 35.0 J
Therefore, the work done on the block by the applied force is 35.0 J (joules).
To find the work done by the force of gravity on the block as it moves up the incline, we need to calculate the component of gravity that acts along the direction of motion and multiply it by the distance moved.
1. First, let's find the component of the weight that acts along the incline. This can be calculated using the formula:
Weight along the incline (Wx) = Weight * sin(θ)
Wx = 25.0 N * sin(34.0°)
2. Next, we can calculate the work done by gravity using the formula:
Work by gravity (Wg) = Weight along the incline * distance
Wg = Wx * 2.50 m
To find the work done by the applied force on the block as it moves up the incline, we can use the formula:
3. Work by the applied force (Wf) = Force * distance
Wf = 14.0 N * 2.50 m
Now we can calculate the values:
1. Wx = 25.0 N * sin(34.0°)
2. Wg = Wx * 2.50 m
3. Wf = 14.0 N * 2.50 m
By substituting the values in these equations, we can find the work done by the force of gravity and the applied force on the block as it moves up the incline.