A crate of mass 48 kg is pushed up a frictionless ramp by a person as shown in the figure below. Calculate the work done by the person in pushing the crate a distance of 11 m as measured along the ramp. Assume the crate moves at constant velocity. _____J
To calculate the work done by the person in pushing the crate up the ramp, we need to use the formula for work:
Work = Force × Distance × cos(θ)
Where:
Force is the component of the force acting in the direction of motion,
Distance is the distance traveled,
θ is the angle between the force and the direction of motion.
In this case, the crate moves at a constant velocity, which means there is no acceleration. Therefore, the net force acting on the crate is zero, which means the force of gravity is balanced by the force exerted by the person pushing. Thus, the force exerted by the person is equal in magnitude and opposite in direction to the force of gravity acting on the crate.
The force of gravity can be calculated using the formula:
Force of gravity = Mass × Acceleration due to gravity
Given that the mass of the crate is 48 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we get:
Force of gravity = 48 kg × 9.8 m/s^2 = 470.4 N
Since the crate is moving at a constant velocity, the force exerted by the person must be equal in magnitude and opposite in direction to the force of gravity. Therefore, the force exerted by the person is also 470.4 N.
The distance traveled along the ramp is given as 11 m.
Using the formula for work, we can now calculate the work done by the person:
Work = Force × Distance × cos(θ)
Since the force exerted by the person is in the same direction as the displacement, the angle (θ) between them is 0 degrees. The cosine of 0 degrees is 1.
Therefore, the work done by the person is:
Work = 470.4 N × 11 m × cos(0°)
Work = 470.4 N × 11 m × 1
Work = 5174.4 J
Therefore, the work done by the person in pushing the crate a distance of 11 m along the ramp is 5174.4 Joules.
To calculate the work done by the person in pushing the crate, we need to determine the force exerted by the person and the distance over which the force is applied.
In this case, since the crate is moving at a constant velocity, we know that the net force acting on it is zero. This means that the force exerted by the person upwards along the ramp must be equal in magnitude and opposite in direction to the force of gravity pulling the crate downwards.
The force of gravity can be calculated using the equation F = m * g, where m is the mass of the crate and g is the acceleration due to gravity (approximately 9.8 m/s^2).
F = 48 kg * 9.8 m/s^2
F = 470.4 N
Since the crate is moving at a constant velocity, the force exerted by the person must be equal in magnitude and opposite in direction to the force of gravity:
Force exerted by the person = 470.4 N
Now, we can calculate the work done by the person using the formula W = F * d * cos(theta), where W is the work done, F is the force exerted, d is the distance over which the force is applied, and cos(theta) is the angle between the force and direction of motion.
In this case, since the crate is being pushed up the ramp, the angle between the force exerted by the person and the direction of motion is 0 degrees, and cos(0) = 1.
W = 470.4 N * 11 m * cos(0)
W = 5154.4 J
Therefore, the work done by the person in pushing the crate a distance of 11 m along the ramp is 5154.4 J.