A 15.3 kg block is dragged over a rough, horizontal
surface by a constant force of 130 N
acting at an angle of 26.4◦
above the horizontal.
The block is displaced 16 m, and the
coefficient of kinetic friction is 0.1.
Find the work done by the 130 N force. The
acceleration of gravity is 9.8 m/s^2
Answer in units of J
Find the magnitude of the work done by the force of friction
To find the work done by the 130 N force, you would need to compute the component of the force that is in the direction of the displacement and then multiply it by the displacement.
Step 1: Find the component of the force in the direction of displacement.
- The component of the force in the direction of displacement can be found using trigonometry. Since the force is acting at an angle of 26.4° above the horizontal, we need to find the horizontal component of the force.
- The horizontal component can be calculated using the equation: F_horizontal = F * cos(theta), where F is the magnitude of the force (130 N) and theta is the angle (26.4°).
- Plugging in the values, we get: F_horizontal = 130 N * cos(26.4°).
Step 2: Determine the work done by the force.
- The work done by the force can be found using the equation: Work = Force * Displacement.
- In this case, the force acting in the horizontal direction is F_horizontal and the displacement is given as 16 m.
- Plugging in the values, we get: Work = F_horizontal * Displacement, which becomes Work = (130 N * cos(26.4°)) * 16 m.
Now, we can calculate the work done by the 130 N force.
Step 3: Substitute the values and solve the equation.
- Work = (130 N * cos(26.4°)) * 16 m
- Use a calculator or a mathematical software to evaluate this expression.
- The result will be the work done by the 130 N force in units of Joules (J).
To find the magnitude of the work done by the force of friction, you would need to calculate the work done by the force of friction.
Step 1: Calculate the force of friction.
- The force of friction can be calculated using the equation: F_friction = coefficient of friction * normal force.
- In this case, the coefficient of friction is given as 0.1 and the normal force can be calculated as the weight of the block.
- The weight of the block can be found using the equation: weight = mass * acceleration due to gravity.
- The mass of the block is given as 15.3 kg and the acceleration due to gravity is 9.8 m/s².
- Plugging in the values, we get: weight = 15.3 kg * 9.8 m/s².
Step 2: Determine the work done by the force of friction.
- The work done by the force of friction can be found using the equation: Work_friction = force of friction * displacement.
- In this case, the force of friction is F_friction and the displacement is given as 16 m.
- Plugging in the values, we get: Work_friction = F_friction * 16 m.
Now, we can calculate the magnitude of the work done by the force of friction.
Step 3: Substitute the values and solve the equation.
- Work_friction = F_friction * 16 m
- Use a calculator or a mathematical software to evaluate this expression.
- The result will be the magnitude of the work done by the force of friction.