Suppose you carry a bag of groceries weighing 127 N from your car to your kitchen, a distance of 48 m, without raising or lowering the bag.
(a) What is the work done by the force you exert on the bag?
The force you exert on the bag is equal and opposite to the weight force. The motion is in a perpendicular direction.
When force and motion are in perpendicular directions, the work done is zero.
Well, carrying groceries isn't exactly a barrel of laughs, but I'll give it a go!
Since you're not raising or lowering the bag, we can assume that you're applying a horizontal force. Work is calculated by multiplying the force applied with the distance over which it is exerted. So, the work done by your force can be calculated as:
Work = Force x Distance
Given that the force you exert on the bag is 127 N, and you carried it a distance of 48 m, we can plug them into the equation:
Work = 127 N x 48 m
And when we crunch the numbers, we get:
Work = 6,096 N•m
So, the work done by your force is 6,096 joules (or N•m).
Now that we've done the math, I guess you could say that carrying groceries is quite the "workout"!
To find the work done by the force you exert on the bag, you need to use the formula:
Work = Force × Distance × Cos(theta)
Where:
- Work is the amount of work done (in joules, J)
- Force is the force you exert on the bag (in newtons, N)
- Distance is the distance you carry the bag (in meters, m)
- theta is the angle between the direction of force and the direction of displacement. In this case, since you're not raising or lowering the bag, theta is 0 degrees or 180 degrees.
Given:
- Force = 127 N
- Distance = 48 m
- theta = 0 degrees or 180 degrees (since you're not raising or lowering the bag)
Using the formula, we can calculate the work done:
Work = 127 N × 48 m × cos(0 degrees or 180 degrees)
= 127 N × 48 m × cos(0)
= 127 N × 48 m × 1
= 6096 J
Therefore, the work done by the force you exert on the bag is 6096 joules (J).
To calculate the work done by the force you exert on the bag, you can use the equation:
Work = Force × Distance × cos(θ)
Where:
- Work is the amount of work done by the force (in joules, J).
- Force is the magnitude of the force exerted on the bag (in newtons, N).
- Distance is the displacement of the bag (in meters, m).
- θ is the angle between the direction of the force and the displacement. Since the bag is not being raised or lowered, the angle is 0 degrees, and therefore cos(θ) = 1.
Now, let's calculate the work done. In this case, the force exerted on the bag is the weight of the bag, which is given as 127 N, and the distance the bag is being moved is 48 m.
Thus, the equation becomes:
Work = 127 N × 48 m × cos(0°)
Since cos(0°) = 1, the equation simplifies to:
Work = 127 N × 48 m × 1
Now, you can solve the equation:
Work = 6,096 J
Therefore, the work done by the force you exert on the bag is 6,096 joules.