How much work did the movers do to push a 49.0 kg crate 10.3 m across a rough floor at a speed of 2.9 m/s with a horizontal pushing force of 48 N ?
F*d = 48 * 10.3 =
To determine the work done by the movers, we can use the equation:
Work = force * distance * cos(theta)
In this case, the force applied by the movers is horizontal, so the angle (theta) between the force and the displacement is 0 degrees. Therefore, cos(theta) = 1.
Given:
Mass of the crate (m) = 49.0 kg
Distance moved (d) = 10.3 m
Speed of the crate (v) = 2.9 m/s
Horizontal pushing force (F) = 48 N
First, let's find the acceleration of the crate using the equation:
v² = u² + 2ad
Rearranging the equation, we get:
a = (v² - u²) / (2d)
Where:
u = initial velocity (u = 0, as the crate starts from rest)
Substituting the given values, we find:
a = (2.9 m/s)² / (2 * 10.3 m)
a = 0.452 m/s²
Next, let's find the net force acting on the crate using Newton's second law:
F = m * a
Substituting the given values, we get:
F = (49.0 kg) * (0.452 m/s²)
F = 22.148 N
Since the force applied by the movers is greater than the net force, we can use the net force to calculate the work done:
Work = F * d * cos(theta)
Work = (22.148 N) * (10.3 m) * (1)
Work ≈ 228.0344 Joules
Therefore, the movers did approximately 228.0344 Joules of work to push the 49.0 kg crate 10.3 m across the rough floor at a speed of 2.9 m/s with a horizontal pushing force of 48 N.
To calculate the amount of work done by the movers, you can use the equation:
Work = Force × Distance
Given information:
Mass of the crate (m) = 49.0 kg
Distance (d) = 10.3 m
Speed (v) = 2.9 m/s
Horizontal pushing force (F) = 48 N
First, we need to calculate the acceleration of the crate using Newton's second law of motion:
Force = Mass × Acceleration
Rearranging the equation, we have:
Acceleration = Force / Mass
Plugging in the values, we get:
Acceleration = 48 N / 49.0 kg
Next, we can calculate the acceleration and the time taken to cover the distance by using the equation:
Distance = Initial Velocity × Time + (1/2) × Acceleration × Time²
Rearranging the equation, we can solve for time:
Time = (Final Velocity - Initial Velocity) / Acceleration
Plugging in the values, we have:
Time = (2.9 m/s - 0 m/s) / (48 N / 49.0 kg)
Now, we can calculate the work done by the movers using the equation:
Work = Force × Distance
Plugging in the given values, we get:
Work = 48 N × 10.3 m
Performing the calculation, we find:
Work = 494.4 Joules
Hence, the movers did 494.4 Joules of work to push the crate.