determine the work done in pushing a 100kg wooden block 30 across a horizontal cocerete from with coeficient kinetic=0.48
Given m=100kg g=10m/s^2 s=30m coeficient kinetic=0.48 Req Wf=? Solution Wf=coeficient kinetic mgs Wf=0.48x100kgx10m/s^2x30m Wf=48x300J=14400J
To determine the work done in pushing the wooden block, we can use the formula for work:
Work = Force × Distance × cos(θ)
Where:
- Force is the applied force acting on the object
- Distance is the displacement of the object
- θ is the angle between the direction of the force and the direction of displacement
In this case, the wooden block is being pushed horizontally, so the angle θ between the applied force and the displacement is 0 degrees, and cos(0) is 1.
Given:
- Mass of the wooden block (m) = 100 kg
- Coefficient of kinetic friction (µk) = 0.48
- Distance pushed (d) = 30 m
First, let's calculate the force of kinetic friction acting against the block's motion:
Force of kinetic friction (Fk) = µk × Fnorm
Where:
- Fnorm is the normal force acting on the block
The normal force (Fnorm) can be calculated as:
Fnorm = mass × gravity
Where:
- Gravity (g) = 9.8 m/s^2
Fnorm = 100 kg × 9.8 m/s^2 = 980 N
Now we can calculate the force of kinetic friction:
Fk = 0.48 × 980 N = 470.4 N
Since the applied force is equal in magnitude but opposite in direction to the force of kinetic friction, we have:
Force = - Fk = -470.4 N
Finally, we can calculate the work done:
Work = Force × Distance × cos(θ)
Work = -470.4 N × 30 m × cos(0°)
Work = -470.4 N × 30 m × 1
Work = -14,112 Joules
The negative sign indicates that work is done against the force of friction, which opposes the direction of motion.
To determine the work done in pushing the wooden block, you need to know two things: the force applied and the distance over which the force is applied.
The force required to push an object can be calculated using the equation:
Force = frictional force
The frictional force can be found using the equation:
frictional force = coefficient of kinetic friction * normal force
The normal force acting on the wooden block can be calculated by:
normal force = mass * gravity
where mass is the mass of the block and gravity is the acceleration due to gravity (approximately 9.8 m/s²).
Once you have calculated the force, you can determine the work done using the formula:
Work = force * distance
Given:
Mass of the wooden block (m) = 100 kg
Coefficient of kinetic friction (μ) = 0.48
Distance (d) = 30 m
Step 1: Calculate the normal force.
normal force = mass * gravity
normal force = 100 kg * 9.8 m/s²
normal force = 980 N
Step 2: Calculate the frictional force.
frictional force = coefficient of kinetic friction * normal force
frictional force = 0.48 * 980 N
frictional force = 470.4 N
Step 3: Calculate the work done.
Work = force * distance
Work = frictional force * distance
Work = 470.4 N * 30 m
Work = 14,112 J (joules)
Therefore, the work done in pushing the wooden block 30 m across the horizontal concrete floor is 14,112 joules.