A 10.0kg crate initially at rest on a floor with a static and kinetic coefficient of 0.20 is pushed with a force of 15 N for 4,0 s. the work done is
Work is defined as the force applied multiplied by the distance traveled in the direction of the force. In this case, the crate is pushed horizontally, so we need to calculate the distance traveled by the crate.
To find the distance traveled, we can use the equation: distance = (initial velocity)(time) + (1/2)(acceleration)(time^2)
Here, the crate starts at rest, so the initial velocity is 0 m/s. The acceleration can be calculated using the formula: acceleration = force / mass.
Given:
Mass = 10.0 kg
Force = 15 N
Acceleration = Force / Mass
Acceleration = 15 N / 10.0 kg
Acceleration = 1.5 m/s^2
Using the formula for distance:
distance = (0 m/s)(4.0 s) + (1/2)(1.5 m/s^2)(4.0 s)^2
distance = 0 m + (1/2)(1.5 m/s^2)(16 s^2)
distance = (1/2)(1.5 m/s^2)(16 s^2)
distance = (1/2)(1.5 m/s^2)(256 s^2)
distance = (0.75 m/s^2)(256 s^2)
distance = 192 m
Now, we can calculate the work done using the formula: work = force * distance
Work = 15 N * 192 m
Work = 2880 N·m or 2880 Joules
Therefore, the work done on the crate is 2880 Joules.
A 10.0kg crate initially at rest on a floor with a static and kinetic coefficient of 0.20 is pushed with a force of 15 N for 4.0 s. the work done is
The work done on the crate can be calculated using the formula: work = force * distance
To find the distance traveled by the crate, we need to determine if it remains at rest or if it starts to move. If the applied force is greater than or equal to the static friction, the crate will start to move. Otherwise, the crate will continue to remain at rest.
The static friction can be calculated using the equation: static friction = static coefficient * normal force
The normal force acting on the crate is equal to the weight of the crate, which can be calculated using the equation: weight = mass * gravity
Given:
Mass = 10.0 kg
Static coefficient = 0.20
Force = 15 N
Time = 4.0 s
Gravity is approximately 9.8 m/s^2.
Weight = mass * gravity
Weight = 10.0 kg * 9.8 m/s^2
Weight = 98.0 N
Static friction = static coefficient * normal force
Static friction = 0.20 * 98.0 N
Static friction = 19.6 N
Since the applied force (15 N) is less than the static friction (19.6 N), the crate will remain at rest. Therefore, no work is done on the crate.
Thus, the work done on the crate is 0 Joules.
To calculate the work done, we can use the formula:
Work = Force × Distance × cos(θ)
Where:
Force = 15 N (applied force)
Distance = ? (distance over which the force is applied)
θ = 0° (angle between the force and displacement)
Since the crate is initially at rest and is pushed for 4.0 s, we can use the formula for distance:
Distance = 0.5 × acceleration × time^2
Where:
acceleration = (Net force) / (mass)
The net force acting on the crate can be calculated using the equations for static and kinetic friction:
Static friction force = (Static friction coefficient) × (Normal force)
Normal force = (mass) × (acceleration due to gravity)
Kinetic friction force = (Kinetic friction coefficient) × (Normal force)
The static friction force must be overcome before the crate starts moving, so the applied force of 15 N must be greater than the static friction force. Once the crate is moving, the applied force must overcome the kinetic friction force.
Let's calculate the distance and work done step-by-step:
1. Calculate the normal force:
Normal force = (mass) × (acceleration due to gravity)
Normal force = (10.0 kg) × (9.8 m/s^2)
Normal force = 98.0 N
2. Calculate the static friction force:
Static friction force = (Static friction coefficient) × (Normal force)
Static friction force = (0.20) × (98.0 N)
Static friction force = 19.6 N
3. Check if the applied force is greater than the static friction force:
15 N > 19.6 N
Since the applied force is less than the static friction force, the crate will not move.
4. Calculate the distance:
Distance = 0.5 × acceleration × time^2
Since the crate does not move, the distance is 0.
5. Calculate the work done:
Work = Force × Distance × cos(θ)
Work = 15 N × 0 × cos(0°)
Work = 0 Joules
Therefore, the work done on the crate is 0 Joules.