A 1.7 kg block is moved at constant speed over a surface for which the coefficient of kinetic friction is 0.27. The displacement is 2 m. It is pushed by a force directed at 25 degrees below the horizontal.
Find the work done on the block by: the force. How do you find the force?
Because the block moves at costant speed, the friction force F satisfies the equation
F cos25 = 0.27 M*g = 4.50 N
Solve that for F and multiply the result by 2 m for the work done, in Joules.
ive been trying that but it doesnt work. for the force i get 4.96 and i find the work with that and its always wrong.
To find the work done on the block by the force, we can use the formula:
Work = Force x Distance x cos(theta)
In this case, the force is the force applied to push the block, the distance is the displacement of the block, and theta is the angle below the horizontal.
First, let's find the force.
The force can be found using the equation for the force of friction:
Force of friction = coefficient of friction x Normal force
The normal force can be calculated as the weight of the block, which is given by:
Weight = mass x gravity
Weight = 1.7 kg x 9.8 m/s^2 = 16.66 N
Normal force = Weight = 16.66 N
Now, we can calculate the force of friction:
Force of friction = 0.27 x Normal force
Force of friction = 0.27 x 16.66 N = 4.5 N
The force pushing the block is the horizontal component of the applied force.
Force = Applied force x cos(theta)
Given that theta is 25 degrees below the horizontal, the angle above the horizontal is 180 - 25 = 155 degrees. So, theta = 155 degrees.
Force = Applied force x cos(155 degrees)
Now, we can solve for the applied force.
Applying a force in the horizontal direction will cancel out the force of friction, thus allowing the block to move at a constant speed. Therefore,
Force = Force of friction
Applied force x cos(155 degrees) = 4.5 N
Now, we can find the applied force.
Applied force = 4.5 N / cos(155 degrees)
Using a calculator, we find:
Applied force ≈ 10.83 N
Now, to find the work done on the block by the force, we can substitute the values into the work formula:
Work = Force x Distance x cos(theta)
Work = 10.83 N x 2 m x cos(155 degrees)
Again, using a calculator, we find:
Work ≈ -19.57 J
The work done on the block by the force is approximately -19.57 Joules.
To find the work done on the block by the force, you first need to find the magnitude of the force acting on the block. Here's how you can find it:
1. Draw a free body diagram of the block:
- Represent the weight of the block acting vertically downward with a force of magnitude mg, where m is the mass of the block and g is the acceleration due to gravity (9.8 m/s^2).
- Represent the normal force exerted by the surface on the block acting vertically upward, which is equal in magnitude to mg in this case since the block is not accelerating vertically.
- Represent the force of kinetic friction acting horizontally in the opposite direction of the displacement.
- Represent the applied force acting at 25 degrees below the horizontal.
2. Break down the applied force into its vertical and horizontal components:
- The vertical component of the force is given by: F_vertical = (magnitude of applied force) * sin(25°)
- The horizontal component of the force is given by: F_horizontal = (magnitude of applied force) * cos(25°)
3. Set up an equation in the horizontal direction:
- The force of kinetic friction is given by: F_friction = (coefficient of kinetic friction) * (normal force)
- Since the block is moving at constant speed, the applied horizontal force must be equal to the force of kinetic friction: F_horizontal = F_friction
4. Substitute the values into the equation to solve for the magnitude of the applied force:
- F_horizontal = (0.27) * (mg)
- (magnitude of applied force) * cos(25°) = (0.27) * (mg)
- (magnitude of applied force) = (0.27) * (mg) / cos(25°)
5. Calculate the magnitude of the force:
- Substitute the values of m and g, and compute the magnitude of the force.
After finding the magnitude of the force, you can calculate the work done on the block by the force using the formula:
Work = (magnitude of the force) * (displacement) * cos(theta),
where theta is the angle between the force and the displacement. In this case, theta is 25°.